MR.AHMED HEKAL

PHYSICS 3RD SECONDARY CHAPTERS (1-7)

Mr. Ahmed Hekal

1

Chapter 1

A. Definitions 1- Electrical current:

- Electrons movement through a conductor from negative pole to positive pole in the presence of electric

source

2- Traditional Electrical current:

- Movement of positive charges through a conductor from positive pole to negative pole

3- Current intensity:

- Quantity of electrical charges through a section of a conductor in 1 second

4- Ampere:

- Current intensity results in passing quantity of charges of 1 Coulomb through a conductor in 1 second

5- Coulomb

- The quantity of electrical charges that when passes through a conductor in time of 1 second it generates

current of 1 Ampere

6- Potential difference:

- The work done in joule used to transfer quantity of charges of 1 C between 2 points

7- Volt:

- The potential difference bet. 2 points when work done of 1 J used to transfer quantity of charges of 1 C

8- Electromotive Force:

- The whole work done outside and inside the battery to transfer 1 coulomb of charges in the electrical circuit

- Potential difference between the poles of the battery in case of open circuit

9- Electrical Resistance:

- The opposition الممانعة to the flow of the current

- The ratio between potential difference in volt across the terminals of conductor and current intensity that

flows through this conductor in ampere

10- Ohm’s Law:

- At constant temperature, current intensity is directly proportional with potential difference

11- Ohm:

- The resistance of conductor that allows passage current of 1 Ampere when potential difference across

terminals of this conductor is 1 volt

12- Resistivity:

- It’s the resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperature

13- Conductivity:

- The reciprocal of resistivity

- Reciprocal of resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperature

14- Kirchhoff’s first low:

- In a closed circuit, summation of currents entering a point is equal to summation of currents exiting this

point

- The algebraic summation of currents in a specific point in closed circuit equals zero

15- Kirchhoff’s second law:

- Algebraic summation of e.m.f. in a closed circuit equals the algebraic summation of potential differences in

this circuit

- Algebraic summation of potential differences in a closed branch equal zero

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B. What’s meant by? 1- Current intensity passes through a conductor is 5 A

- The quantity of electrical charges that passes through a section of this conductor in 1second equals 5

coulombs

2- Potential difference between terminals of a conductor is 20 V

- The work done to transfer 1 C of charges bet. terminals of this conductor is 20 Joule

3- Electromotive force of a battery = 1.5 V

- The whole work done outside and inside the battery to transfer 1 coulomb of charges in the circuit = 1.5

joule

4- Electrical Resistance of a conductor 100 Ohm

- The ratio between potential difference across the terminals of conductor and current intensity that flows

through this conductor is 100 V/A

5- Resistivity of a conductor = 6 *10-6 ohm.m

- Resistance of a conductor of this material of length 1 m and cross sectional area of 1 m2 at a constant temp.

is 6 *10-6 ohm

6- Conductivity of material is 5.6 *107 ohm-1.m-1

- Reciprocal of resistance of conductor of length 1 m and cross sectional area of 1 m2 at constant temperature

Is 5.6 *107 ohm-1

C. Deductions 1- Resultant resistance of group of resistances connected in series

- Current intensity is constant through all resistances

- Potential difference is divided between them

V = V1 + V2 + V3

V = I R

I R` = I R1 + I R2 + I R3

Then

2- Resultant resistance of group of resistances connected in parallel

- Potential difference is constant across all resistances

- Current intensity is divided between resistances

I = I1 + I2 + I3

I = V / R

V / R` = V / R1 + V / R2 + V / R3

Then

R` = R1 + R2 + R3

1 / R` = 1 / R1 + 1/ R2 + 1 / R3

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D. Factors that depends on Physical quantity Factors that this quantity depends on

Resistance of a conductor

R = Ꝭe L/A

1- Length of conductor (directly proportional) 2- Its cross sectional area A (inversely

Proportional) 3- Material type of this conductor 4- Temperature of this conductor

Resistivity of conductor 1- Material type of this conductor 2- Temperature of this conductor

Conductivity of a conductor

1- Material type of this conductor 2- Temperature of this conductor

F. Comparisons

resistances connected in series resistances connected in parallel

Shape of connection

Target

To obtain a large resultant resistance from a group of small resistances

To obtain a small resultant resistance from a group of large resistances

Current intensity Equal or constant in all resistances The whole current equals the summation of all currents in all resistances

Potential difference The whole P.D. equals the summation of all P.D.s in all resistances

V = V1 + V2 + V3

Equal or constant across all resistances

Law of resultant

If all resistances are equal

R` = N R Where N is number of them

R` = R / N

R` = R1 + R2 + R3 1 / R` = 1 / R1 + 1/ R2 + 1 / R3

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E. What Happens in these cases 1- Increasing potential difference to double value for current intensity and power consumed?

- Current intensity will increase to double as I = V / R

- Power will increase 4 times as Pw = V2 / R

2- Current intensity increases to double for the resistance value

- Resistance remains constant as it doesn’t depends on current it depends on

- Length of conductor (directly proportional)

- Cross sectional area A (inversely Proportional)

- Material type

- Temperature

3- Increasing cross sectional area of a conductor to double and decreasing its length to half value for the

resistance

- L1 = 2 L , L2 = L , A1= A , A2 = 2 A

- R1 / R2 = L1 A2 / L2 A1 = 2 L * 2 A / L * A

- R2 = ¼ R1

4- Connecting two resistance in parallel on of them has a value of 1 ohm to the resultant resistance

- Resultant resistance will be less than 1 ohm

5- Current doesn’t flow from an electric source to potential difference between the terminals of this electric

source

- Potential difference between the terminals of this electric source will be equal to electromotive force of the

electric source according to this relation

(V = VB – I r) and I = 0 then V = VB

F. Give reason 1- Work should be done to transfer charges from point to point

- To get rid of resistance bet. the two points and current can flow

2- Some materials can conduct electricity but others cannot

- As some materials have a plenty of free electrons so it allows flow of current while other materials don’t

have free electrons or their electrons are strongly correlated to their atoms

3- Increasing radius of a wire of copper leads to decreasing its resistance to quarter value

- According to this relation

R = Ꝭe l/r2

Resistance is inversely proportional with square of radius

4- When a conductor is shaped to be parallelogram its ribs resistances are different while if shaped as a

cube its ribs resistances are equal

- As ribs of parallelogram are different in length so their resistance differs according to relation

R = Ꝭe l/A but cube ribs are equal in length and equal in resistance 5- Resistance increase when increasing temperature

- When raising temperature this increase the speed of vibrating its molecules and increase the rate of

collisions between electrons of current and conductor molecules so the opposition الممانعة of current

increases

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6- Resistivity of a conductor is a physical property

- As it depends on the type of the conductor material at constant temperature

7- Conductivity of a conductor is a physical property

- Because conductivity is the reciprocal of resistivity which depends on the conductor material at constant

temperature 8- Conductivity factor of copper is large

- As resistivity of copper is very small in cause of plenty of free electrons in copper

9- It’s preferred to use wires of copper in the electrical connections

- As resistivity of copper is very small so its resistance is low and this prevent wire from consuming electrical

energy

10- Home devices are connected in parallel

- All devices will work on the same potential difference of the source so each device can work alone and if

one of them damaged it doesn’t affect the others and also to decrease their total resistance which doesn’t

affect the main current

11- Home devices aren’t connected in series

- Because potential difference will be divided across them which leads to a probability of insufficient voltage

on a device that cannot operate and one device cannot work alone also their total resistance will be huge

which prevents the current from passing through the circuit

12- The electrical power increases in case of connecting two resistance on parallel

- When connecting resistances in parallel their total resistance decreases and current will increase and Power

also will increase according to this law Pw= IV

13- In a circuit of parallel connection resistances we use thick wires at the terminals of battery and thin

wires at the terminals of each resistance

- As current intensity should be maximum at the input and output of the battery so we use thick wires of low

resistance while current is divided through each resistance so we can use thin wires in terminals of each

resistance

14- Potential difference between battery poles increases when increasing resistance of its circuit

- According to this relation (V = VB – I r) when increasing resistance current will decrease and the internal

potential difference (I r) will decrease and because VB is constant then potential difference across the

battery will increase

15- E.M.F of a battery is larger than potential difference between its outer terminals when closing the

switch

- Because the internal resistance of the battery consumes power to allow current to flow inside it so

(VB = V + I r) so VB > V

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Mr. Ahmed Hekal

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Laws

To compare between Power consumed in two

resistances

When V is constant

(Pw)1 / (Pw)2 = R2 / R1

When current is constant

(Pw) 1 / (Pw)2 = R1 / R2

Resistance

R = V / I

R = Pw / I2

R= V2/Pw

R = Ꝭe L/A = Ꝭe L/r2

Ꝭ (density) = m (mass) / v (volume)

Ꝭ = m / v

And v = L * A and L = v / A

Then Ꝭ = m / L A then

A = m / L Ꝭ and

L = m / A Ꝭ

R = Ꝭe L2 Ꝭ / m

R = Ꝭe v (volume) / A2

R = Ꝭe L2/ v (volume) Compare between resistances

R = Ꝭe m / Ꝭ A2

R1/R2= Ꝭe1 L1 A2 / Ꝭe2 L2 A1

R1/R2 = Ꝭe1 Ꝭ1 L12 m2 / Ꝭe2 Ꝭ2 L2

2 m1

R1/R2 = Ꝭe1 L1 r22 / Ꝭe2 L2 r1

2

Conductivity

σ = 1 / Ꝭe= L / R A

Laws

Quantity of charges

Q = I t

Q = n qe

Q = W / V

Q: total quantity of charges (electrons)

n: number of electrons

qe: charge of one electron

W: work done

V: potential difference

I: current intensity

t: time

Potential difference V

V = W / Q

V = W / nqe

V = I R

V = Pw / I

Current Intensity

I = Q / t

I = n qe / t

I = V / R

I = Pw / V

Electrical Power

Pw = W / t

Pw = V I

Pw = I2 R

Pw = V2 / R

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Mr. Ahmed Hekal

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To Solve Kirchhoff’s Problems follow the following:

1- Divide the circuit to no. of loops (2 or 3 loops)

2- Find a point (junction) in which all currents are entering or leaving it

3- Write the first equation using Kirchhoff’s first law (sum of currents entering a point equals to sum o

currents leaving this point

4- Specify my direction as follow

A. If there is one battery in the loop, specify the direction to be from +ve pole to –ve pole of this

battery

B. If there are two batteries in the loop, specify the direction to be from +ve pole to –ve pole of

the largest battery

5- Write the 2nd and 3rd equations using Kirchhoff’s second law (sum of potential difference inside a

loop equals zero), we have two choices:

A. If there is one battery in the loop, then write its value direct V= IR + IR

B. If there are two batteries in the loop, then we have two choices

If they are connected parallel ( -ve connected to –ve and +ve connected to +ve) then

subtract their values V1-V2 = IR +IR

If they are connected in series ( -ve connected to +ve and +ve connected to negative)

Then add their values to each other V1+V2= IR +IR

C. The sign of IR depends on the direction of the current

If the current passes in the same direction of my direction then put it in +ve (+IR)

If the current passes in the opposite direction of my direction then put it in –ve (-IR)

6- Current that leaves the battery is the same current enters the battery

7- Potential difference between two points is equal to the potential (or voltage) at the point of higher

potential the potential (or voltage) at the point of lower potential

8- Solve the 3 equations using calculato

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Chapter 2

G. Definitions 16- Magnetic Flux:

- Number of magnetic field lines of a magnet from north pole to south pole

17- Magnetic flux density at a point:

- It’s the magnetic flux for unit area which is normal to magnetic lines around this point

Or

- The magnetic force affecting a wire of 1 m length placed normal to magnetic flux and a current of 1 A

passes through it

18- Tesla

- The magnetic flux density that generates a force of 1 Newton on a wire of 1 m length and a current of 1A

passes through it when this wire is normal to the flux lines

19- Permeability coefficient of a medium:

- The ability of medium to permit the magnetic flux through it

20- Dipole Moment :

- It’s the magnetic torque affecting a coil placed parallel to magnetic field of 1 tesla when an electrical current

passes through it.

21- Moving Coil Galvanometer (sensitive Galvanometer):

- A device used to detect a very weak current to measure its intensity and determine its direction

22- Galvanometer sensitivity:

- The deviation angle of its pointer from zero position when a current of 1 A passes through it

23- Shunt Resistance

- A small resistance connected in parallel with galvanometer to convert it to an ammeter to measure higher

currents

24- Ammeter Sensitivity

- Ratio between maximum current measured by galvanometer to maximum current measured after

converting it to ammeter

25- Multiplier Resistance:

- Large resistance connected in series with galvanometer to convert it to voltmeter to measure higher

voltages

H. What’s meant by? 7- Flux density at a point is 0.4 Tesla

- It means that a magnetic force of 1 N is affecting a wire of 1m length placed normal to the magnetic flux at

this point and a current of 1 A passes through it

8- Dipole Moment is 0.7 N.m/T

- It means that magnetic torque of 0.7 N.m is affecting a coil when a current passes through it and this coil is

placed parallel to a magnetic flux of 1 tesla

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I. Figures

J. Conditions needed to :

Attraction force bet. two wires having currents pass through them

The two currents should be in the same direction

Repulsion force bet. two wires having currents pass through them

The two currents should be in opposite directions

Flux density vanishes at a point between two parallel wires having currents pass through them

The two currents should be in the same direction

Neutral point exists between two straight parallel wires in a mid-point between them

The two currents should be equal values and in the same direction

Impossibility of existence of a neutral point for two straight parallel wires having currents pass through them

The two currents are equal values and are in opposite directions

Vanishing the Force affecting a wire have a current pass through it inside a magnetic field

Wire is parallel two to the magnetic flux

Vanishing the torque affecting a coil in which a current passes and is placed in a magnetic field

When the plane of the coil is perpendicular to the magnetic flux

K. Devices Device Usage Scientific Idea and explanation

Moving Coil Galvanometer to detect very low DC currents and measures its values and determines its direction

Idea: The torque affecting a rotating coil having a current passes through it inside a magnetic field Explanation: When current passes through the coil, two equal parallel forces are generated in opposite directions on two ribs ضلعين of the coil which causes rotation torque on the coil

Shunt resistance in Ammeter

Converts the galvanometer to Ammeter to measure higher currents

When a small resistance is connected in parallel with the galvanometer coil this leads to decreasing the total resistance of the ammeter which avoid affecting the current needed to be measured

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Multiplier resistance in Voltmeter Converts the galvanometer to Voltmeter to measure higher potential differences

Connecting high resistance in series with a galvanometer leads to increasing the total resistance of it and when connecting this Galvanometer in parallel with the circuit it consumes a very small current then it doesn’t affect the potential difference needed to be measured

L. Usages

Pair of spiral springs in Galvanometer 1- It’s used as connectors to current 2- Control the pointer movement using reverse torque to

indicate the right value 3- Return the pointer to its zero position

The concave poles in Galvanometer They remain the flux density constant in the space in which coil moves, this way ensures that flux lines are always in a radius form and they are parallel to the coil plane (normal to two certain rips)

Iron core inside Galvanometer Collecting and concentrating the flux lines inside the coil

Jeweled bearings in Galvanometer Coil stands on them and they facilitates its rotation

The standards and variable resistance in Ohmmeter

Controls the current intensity to be maximum value which moves the pointer to the end of reading (zero ohm) before adding the resistance needed to be measured

M. Deductions

1- Magnetic force that affects a wire through which electrical current passes in a magnetic field:

-

- F α B (Flux Density) And F α I (current) And F α L (length affected in wire)

- F α BIL

-

Where is the angle between the wire and the flux

Newton = Tesla.ampere.m, Tesla = Newton /ampere.m

F = BIL sinNewton

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2- Torque affecting a rectangle coil through which current passes and is placed inside a magnetic field

- when a coil is placed in a magnetic field and a current passes through it and the plane of the coil is parallel

to the plane of the field

- there are 2 rips are parallel to flux so force is zero, and the other 2 rips are perpendicular to the field so they

are affected by 2 equal and opposite forces not on the same line, this will cause rotation

- rotation happened in cause of torque

- Torque = force * distance

- Force = BIL sin

- Distance = L (the normal distance between the pole and the affected rip) this distance is the wide of the

rectangle

- Torque = B I (Length* width) sin

- Ʈ = B I A sin

- If we have number of turns N in the coil so :

And

= B |md| sin

Where |md| is the dipole moment |md|= I A N

3- Shunt Resistance

- Rs and Rg are connected in parallel so

- Vg = Vs

- Then Ig Rg = Is Rs

- Rs= Ig Rg / Is but Is= I - Is

- Then

4- Multiplier Resistance Rm

- Rm and Rg are connected in series so

- V = Vg + Vm = Ig Rg + Ig Rm

-

-

= B I A N sin

[Cite your source here.]

Rs= Ig Rg / (I - Ig)

Rm= (V – Ig Rg) / Ig

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N. Factors that depends on

Physical quantity Factors that this quantity depends on

Magnetic Flux Density generated from wire at a point

B = d )

1- Current Intensity (directly proportional) 2- Distance bet. the point and wire (inversely

proportional) 3- Permeability coefficient of the medium (directly

proportional)

Magnetic Flux Density generated from coil at the center point

B = r)

3- Number of turns (directly proportional) 4- Current Intensity (directly proportional) 5- Radius of coil (inversely proportional) 6- Permeability coefficient of the medium (directly

proportional)

Magnetic Flux Density generated from Solenoid at a point on its axis

B = L

3- Number of turns (directly proportional) 4- Current Intensity (directly proportional) 5- Axis length (inversely proportional) 6- Permeability coefficient of the medium (directly

proportional)

Magnetic Force

F = BIL sin

1- Magnetic flux density B (directly proportional) 2- Length of affected part of the wire (directly

proportional) 3- Angle between the field and wire (directly

proportional) 4- Current Intensity (directly proportional)

Torque affecting a coil

= B I A N sin

1- Number of turns (directly proportional) 2- Current Intensity (directly proportional) 3- Magnetic flux density B (directly proportional) 4- Angle between the field and wire (directly

proportional) 5- Area of the rectangular coil (directly proportional)

Dipole Moment |md|= I A N

1- Number of turns (directly proportional) 2- Current Intensity (directly proportional) 3- Area of the rectangular coil (directly proportional)

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G. Comparisons

Two wires having a current passes through them

In the same direction In opposite directions

Resultant of flux density at a point in between

B total = B1- B2 where B1> B2 B total = B1+ B2

Resultant of flux density at a point outside them

B total = B1+ B2 B total = B1- B2 where B1> B2

Neutral Point B1 = B2 Falls between the two wires I1 / (x-d) = I2 /d

Where x is the distance bet. Wires and d is the distance bet. the point

and wire of lower current

Falls outside the wires I1 / ( x + d ) = I2 /d

Where x is the distance bet. Wires and d is the distance bet. the point and

wire of lower current

Force between the two wires Attraction Repulsion

- Rules

Ampere Right Hand Rule Right Screw Clock Rule Fleming Left Hand rule

Figure Straight wire

Solenoid

Usage Specifying the direction of magnetic flux generated by a current passes through a wire

Specifying the polarity of the field

Specifying the direction of magnetic flux at center of a coil or solenoid axis

Specifying the pole type (North-South) at the face of a coil or solenoid

Specifying the direction of magnetic force affecting a wire which placed perpendicular to a magnetic field and current passes through it

Working Method

Thumb finger refers to current and other fingers rounding the wire will refer to magnetic flux

Thumb refers to magnetic flux and other fingers rounding the solenoid will refer to the current

When screw rotates in clock-wise direction its rotation refers to the current and its movement direction refers to magnetic flux

If the direction of current in a specific face is clock-wise then this face is South pole and if anti-clock then it will be North pole

Middle finger refers to current ,index finger refers to magnetic flux then the thumb refers to the force

Notice: magnetic flux lines is directed from north to south outside the coil and from south to north inside the coil

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Ammeter, Voltmeter, Ohmmeter

Ammeter Voltmeter Ohmmeter

Function Measuring high currents Measuring potential difference bet. two points

Measuring resistance

Resistance connected on the galvanometer coil

Galvanometer coil is connected in parallel to small resistance called Shunt resistance Rs

Galvanometer coil is connected in series to large resistance called Multiplier Resistance Rm

Galvanometer coil is connected in series to standard resistance Rc and variable resistance Rv and a battery

Idea Of Work Torque affecting a coil that has a current passes through it, this coil is rotating inside magnetic field

Torque affecting a coil that has a current passes through it, this coil is rotating inside magnetic field

Depends on the inverse relation bet. current and resistance at constant potential difference

Law Rs= Ig Rg / (I - Ig)

Rm= (V – Ig Rg) / Ig

I = V / (Rg+ Rc+ Rv+Rx+r)

How it’s connected in circuit

In series In parallel Device terminals is connected to terminals of the external resistance

Graduation Regular as I α Regular as V α Not regular as I α R`+Rx)

Shunt and Multiplier Resistances

Shunt Resistance Multiplier Resistance

Method of connection In parallel with galvanometer coil In series with galvanometer coil

Function Convert the galvanometer to Ammeter to measure higher currents

Convert the galvanometer to Voltmeter to measure higher potential difference

Idea of work By connecting shunt resistance in parallel with the galvanometer this leads to reduce the total resistance of the

device(ammeter) which avoid affecting the current needed to be measured

Connecting high resistance in series with a galvanometer leads to increasing the total resistance of it and when connecting this Galvanometer in parallel with the circuit it consumes a very small current then it doesn’t affect the potential difference needed to be measured

Analog Measuring devices Digital Measuring devices

Its idea depends on Torque affecting a coil that has a current passes through it, this coil is rotating inside magnetic field

Values are appeared on a graduation on which pointer is moving

As Galvanometer, Ammeter ,Voltmeter

Depends on digital electronics

Values are appeared as digits displayed on the screen of the device

As devices of measuring DC and AC currents

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O. What Happens in these cases 1- Current flows in the same direction in two parallel wires

- The resultant of flux densities outside the wires will be larger than it between the wires so attraction force is

generated between them

2- Current flows in opposite directions in two parallel wires

- The resultant of flux densities between the wires will be larger than it outside them so repulsion force is

generated between them

3- Cutting a solenoid of length L and number of turns N at a middle point on its axis and connecting one half

to the same battery

- The solenoid resistance is reduced to half and current intensity will increase to double (and number of turns

remain constant in unit length) so flux density will increase to double

4- Placing wire having a current perpendicularly to a magnetic field

- Wire is being affected by a magnetic force which is perpendicular to current direction and flux lines

5- Passage of dc current of high intensity (bigger than Ig) through the galvanometer coil

- high torque is generated in the coil which is higher than the moment of the ability of the two bearing coils so

they are destroyed and the device is broken down

6- Passage of high frequency (AC) current inside galvanometer

- The pointer is oscillating at the zero reading according to inertia as the pointer cannot react with the change

of direction

7- Reducing the value of shunt resistance

- Ammeter sensitivity is reduced and the graduation of reading is increased

8- Increasing the value of multiplier resistance

- Voltmeter sensitivity is reduced and it will measure higher voltage

9- Nonexistence of standard resistance

- Galvanometer coil will be damaged if current is high and ohmmeter pointer will not be accurate

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P. Give reason 1- It’s recommended in building to be far away the higher voltage towers

- To reduce the effect of the magnetic field which is harmful to the health and environment as the magnetic

flux density is inversely proportional to the distance

2- The neutral point is positioned between two wires having currents pass through them in the

same direction

- Wires will generate two opposite magnetic fields at all points between them so neutral point exists between

them when they vanish each other

3- The neutral point is positioned outside two wires having currents pass through them in opposite

directions

- Because of generating two opposite magnetic fields outside the wires so neutral point exists outside them

when they vanish each other

4- Parallel wires are attracted when currents pass through them in the same direction

- As the resultant flux density between them is lower than it outside them so magnetic force is generated

from the higher density region to lower density region so they are attracted

5- Flux density increases on axis of solenoid that has current passes through it when placing iron core

inside it

- Because permeability coefficient of iron is more than it in air so iron will increase and concentrate the

magnetic flux lines which leads to increase the density

6- Magnetic field in a coil or solenoid may vanish although there is a current passes through it

- As the coil or solenoid is double rounded ,so the magnetic field of one direction is opposing the magnetic

field of the second direction

7- Movement of a straight wire which has electrical current and placed normal to a magnetic field

- This happens according to the difference between the original magnetic field and the field generated by the

wire so wire will move from high density to low density

8- wire having current may not move although it’s placed inside magnetic field

- because it’s placed parallel to magnetic field so (= 0) and F = B I L sin which leads to zero

9- when current passes through a solenoid and a wire placed on its axis, the wire is affected by

magnetic field

- as the wires is placed parallel to magnetic field that is generated by passage of electrical current in the solenoid

And F = B I L sin

10- torque may not be generated on a rectangular coil which has a current and placed into a magnetic

field

- As the coil should be placed parallel to the magnetic field in order to be affected by magnetic force on two

rips which generate the torque, so if it’s placed perpendicular to the field torque will be 0

11- Torque is reduced on the rectangular coil through its rotation starting from parallel position

- At the parallel position the angle between the coil and the normal plane to field equal 90 so torque is

maximum, while rotating the angle is decreased until it reaches 0 at which angle is zero

sin

12- Concave poles in Galvanometer

- To keep the magnetic flux lines always parallel to the coils so at any position magnetic field density will be

constant and the deviation angle will always proportional to current intensity

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13- Coil of galvanometer is connected to couple of bearings coils

- They are used to

A. As connectors of current entering and exiting galvanometer

B. They generate opposite torque used to

. Stop pointer at the right value of current

. Return pointer to zero value after the current disconnected

14- Coil of Galvanometer is placed on jewels bearings

- To reduce frictions and maintain the equilibrium of coil to facilitate the rotation

15- Existence of iron core cylinder inside the coil of galvanometer

- To concentrate and increase the magnetic flux inside the coil which increase the galvanometer sensitivity

16- Graduation of galvanometer is regular and zero reading is positioned in the middle

- As the deviation angle is directly proportional with the current intensity and zero is positioned in the middle

to specify the direction of current

17- Galvanometer cannot measure AC current

- As the magnetic field generated by AC is also alternating so the direction of torque changes each half cycle

so inertia will prevent the reaction to this change

18- Galvanometer doesn’t measure high current intensities

- As its coil cannot bear high currents because part of this current is converted to thermal energy which leads

to melting the coil wire and also the torque generated by higher current is very strong which may damage

the jewels bearings

19- Ammeter is connected in series in the circuit

- To measure the total current of the circuit

20- In Ammeter, a very small shunt resistance is connected in parallel with galvanometer coil

- To reduce the total resistance of device which avoid current decrease and the majority of current will pass

through the shunt resistance which protect the coil from damage so we can use Ammeter in measuring high

currents

21- Voltmeter is connected in parallel in the circuit

- To make the potential difference across the voltmeter equal to the potential difference needed to be

measured

22- In Voltmeter, a very high multiplier resistance is connected in series with galvanometer coil

- To enlarge the resistance of the device so a very small part of current will pass through it and the majority of

current will not affected so potential difference needed to be measured also will not affected

23- Electromotive force of the battery in Ohmmeter circuit should be constant

- To maintain Ohm’s law and make the current always inversely proportional to resistance in case of

constant e.m.f

24- High standard resistance is connected in Ohmmeter circuit

- To reduce the current passing through the circuit to protect the galvanometer coil from damage and make

its pointer deviate to the maximum reading before connecting the unknown resistance

25- Graduation of Ammeter is regular and graduation of Ohmmeter is not regular

- As in Ammeter the deviation angle is directly proportional to the current, but in Ohmmeter the current is

inversely proportional with the total resistance not only the unknown resistance

26- Ammeter graduation opposes the Ohmmeter graduation

- Because the current is inversely proportional with resistance so when adding resistance the current

decreases

-

Mr. Ahmed Hekal

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Laws

2- Flux density in 2 coils

A. In the same level

- Currents in the same direction

BT = B1+ B2

- Currents in opposite direction

BT = B1- B2 (B1>B2)

B. Coils are normal to each other

- B = √B12

+ B22

3- Flux density between a coil and a wire

A. If the current is in the same direction

- BT = Bwire+ Bcoil

B. If the current is in opposite directions

- BT = Bbig- B small

4- To calculate number of turns in a coil

A. If a wire of length L is rounded in

form of coil

- N = L /2r

B. If the coil is less than 1 turn (part of a

turn)

- N = / 360

5- In case of the wire is tangent to the

coil

- N I1 = I2/

6- If a coil of N1 turns is reformed to N2

turns and connected

- B1/B2 = N1r2/N2r1= N12/N2

2= r22/ r1

2

Laws

1- Magnetic Flux m in straight wires

m = 0 when flux is parallel to area

m = B A when flux is normal to area

m = B A sin when flux is making angle

with the area

If the flux rotates with angle from

Parallel position m = B A sin

Normal position m = B A sin (90-

- If the current is in the same direction

- Neutral Point between the wires

I1 / (x-d) = I2 /d

Outside the wires between the wires

BT = B1+ B2 BT = B1- B2 (B1>B2)

- If the current is in the opposite direction

BT = B1- B2 (B1>B2) BT = B1+ B2

- Neutral Point is outside the wires

I1 / (x+d) = I2 /d

-

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Laws

7- Solenoid

- B = µ N I /L = µ n I - If turns are tangent

So: L = N*2 r` - Where :n is the no. of turns per unit area

and r` is the radius of solenoid

8- Solenoid and Coil

Bwire/Bsolenoid = Lsoleoid / 2 rcoil

9- Force

F = B I L Sin

- Between two wires

-

F = L /2d

- Force of two wires affecting third wire

F3= BT I3 L3

- When equilibrium

F = Fg

B I L = mg

10-Torque

= B I A N sin

is the angle between the coil and

the normal plane to the magnetic field

Laws

11- Galvanometer sensitivity =

=Galvanometer sensitivity * number

of divisions

12- Ammeter

- Shunt resistance

Rs= Ig Rg / (I - Ig)

- Ammeter Resistance

R`=Rg. Rs / (Rg +RS)

- Ammeter Sensitivity

Ig/Is = Rs/ (Rs+ Rg)

13- Voltmeter

- Multiplier Resistance

Rm= (V – Ig Rg) / Ig

- Voltmeter Resistance

R`= Rg+ Rm

14- Ohmmeter

To modulate the Ohmmeter

Imax. = V / (Rg+ Rc+ Rv+r)

Rc: is the standard resistance

After adding unknown resistance

I = V / (Rg+ Rc+ Rv+Rx+r)

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Q. Experiments

1- Magnetic field due to a current passes through a straight wire 1) Use iron filings sprinkled on a horizontal cartoon boards

2) Use a wire to penetrate the board vertically

3) Use battery to pass a current in the wire

4) You will notice that iron filings are aligned in circles around a wire

2- Torque produced in a coil placed in a magnetic field 1) Rectangular coil abcd is placed parallel to a regular magnetic field

2) Ribs ad,bc are parallel to flux lines, so there is no force affecting them

3) Ribs ab,cd are normal to flux lines so they are affected by two equal and opposite magnetic forces

equal B I L

4) As a result for these two forces a torque is generated so we noticed that coil will rotate in a

direction specified by using Fleming Left Hand rule for each force

- Middle finger refers to the current

- Index (forefront) finger refers to magnetic field

- Thumb will refer to the force

5) Torque is specified by this relation

= B I Lab Lbc = B I A

When coil has N number of turns so:

= B I A N sin

Where is the angle between the coil and the normal plan on the magnetic field

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Chapter 3

R. Definitions 1- Electromagnetic induction

- The phenomena of producing induced e.m.f and induced current in a conductor as a result of

changing the magnetic flux that’s intersected by this conductor

2- Lenz’s Rule :

- The induced current is in direction to oppose the change that is caused by it

3- Faradays Law:

- Induced e.m.f produced in a coil by electromagnetic induction is directly proportional with the

time in rate of change magnetic flux intersected by the coil and also with number of turns

4- Weber:

- It’s the magnetic flux that is normally penetrating a coil of 1 turn and when it’s vanished gradually

in 1 second an induced e.m.f of 1v is generated in the coil

5- Mutual induction

- The electromagnetic effect between 2 adjacent coils one of them has AC current which affect the

other coil so an induced current is generated in the 2nd coil to oppose the change happened to it

6- Mutual induction coefficient:

- It’s the induced e.m.f generated in a one coil when changing the current in the other coil by rate

of 1 A/S

7- Self-Induction:

- It’s the electromagnetic effect happened in the same coil to oppose the changing of its current

8- self-induction coefficient:

- it’s the induced e.m.f generated in the same coil when its current changes by rate of 1 A.S

9- Henry:

- It’s the mutual induction coefficient between 2 coils when current of one of them changes by rate

of 1 A/S an induced e.m.f of 1v is generated in the other coil

Or

- It’s the self-induction coefficient of a coil when its current changes in rate of 1 A/S an induced

e.m.f of 1v is generated in the same coil

10- Eddy Currents:

- It’s induced currents generated in a metal core as a result of its motion inside a magnetic field or if

it’s exposed to a changing magnetic field

11- Generator (Dynamo)

- A device used to convert mechanical (motion) energy to electrical energy

12- AC current:

- It’s the electrical current that changes its value and direction periodically with time

- It’s the current that changes its value from 0 to max. and returns back to 0 in half cycle then it

reverses its direction and reaches the max. value in opposite direction then returns to 0 again in

another half cycle

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13- Effective value of AC current:

- It’s the dc current intensity that generates the same amount of thermal energy that’s generated

by AC current in the same resistance in the same time

- It’s the dc current intensity that generates the same electrical power that’s generated by the AC

current in the same resistance

14- Transformer:

- A device used to step up or step down the alternating voltage

15- Transformer Efficiency:

- It’s the ratio of secondary coil power to primary coil power

- It’s the ration of the electrical energy produced in the secondary coil to the electrical energy

consumed in the primary coil in the same time

16- Electrical Motor:

- A device used to convert electrical energy to mechanical (motion) energy

S. What’s meant by

T. Figures

U. Conditions needed to :

Generating of directly induced e.m.f or directly induced current in the secondary coil

1- Moving the primary coil away from secondary coil

2- Decreasing the current in the primary coil 3- Open the circuit of the primary coil while it is

near to or inside the secondary coil

Generating of inversely induced e.m.f or inversely induced current in the secondary coil

1- Moving the primary coil near to or inside secondary coil

2- Increasing the current in the primary coil 3- Close the circuit of the primary coil while it is

near to or inside the secondary coil

Generating Eddy currents 1- Moving (rotating) a piece of metal core inside a constant magnetic field

2- Exposing a piece of metal core to a variable magnetic field

Generating a unified directional current but variable in its value in Dynamo (Generator)

1- Replacing the two metal rings with one metal cylinder cracked into two halves this cylinder called current rectifier

Generating DC current in Dynamo (Generator)

1- Using several coils separated by small equal angles

2- Replacing the two metal rings with one metal cylinder cracked into several parts where No. of parts = double No. of coils

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Improving the transformer efficiency 1- Fabricating the coils from metal wires which have a very small resistance to reduce losing of electrical energy in form of heat

2- Fabricating the iron core from insulated slices of wrought iron as it has high resistivity used to reduce Eddy currents

3- The wrought iron is characterized by the ease of moving of its magnetic molecules it leads to reduce losing energy in form of mechanical energy

4- The secondary coil is rolled around the primary coil to prevent leakage منع تسرب of magnetic flux lines of primary coil away from the secondary coil

Improving efficiency of rotating the electrical motor (improving the torque of rotation)

1- Using several coils separated by small equal angles

2- Replacing the two metal rings with one metal cylinder cracked into several parts where No. of parts = double No. of coils

V. Applications of electromagnetic Induction

Device Usage Scientific Idea and explanation

Fluorescent Lamp Lighting Idea: Self-induction in coil Explanation: the magnetic energy stored in the coil will be transferred to a vacuum tube which has inert gas غاز خامل this energy causes collisions between gas atoms so they are ionized and collide with the inner surface of lamp which is plated with fluorescent material so visible light is released

Induction furnaces

Melting metals Idea: Eddy Currents Explanation:

When changing magnetic that’s penetrated by an iron core, induced currents are produced in this core which leads to increase its temperature until melting degree

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Dynamo (Generator) Convert mechanical (motion) energy to electrical energy

Idea: Electromagnetic Induction Explanation: When rotating the coil bet. magnet poles, it intersects variable number of magnetic lines so an induced e.m.f and induced AC currents is generated inside the coil AC current changes its value and direction gradually with time

Electrical Transformer 1- step up or step down the alternating voltage

2- reduce losing energy during its transfer from generators to consumption places through far distances

3- In some home devices

Idea: Mutual Induction bet. 2 coils Explanation: When primary coil is connected to AC source, so the changing in magnetic field will generate induced e.m.f in the secondary coil that will be bigger than or smaller than e.m.f of source according to number of turns in the two coils It enlarges the e.m.f when NP > Ns

It reduces the e.m.f when NP < Ns

Electrical Motor Convert electrical energy to mechanical (motion) energy

Idea: Torque results in passage of electrical current in a coil inside a magnetic field Explanation: When electrical current passes through a coil, two equal and opposite directions forces will affect the two ribs normal to magnetic field so torque is generated which rotates the coil in one direction around its axis

W. Usages

Fleming’s Right Hand Rule Specifies the direction of induced current in a straight wire moves normally to magnetic field

Unified direction and variable intensity electrical current

Preparing some metals by electrical analysis of its compounds

Unified direction and unified intensity electrical current

Mobile phones chargers

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Deductions

5- Faraday’s Law:

Induced e.m.f produced in a coil by electromagnetic induction is directly proportional with the time rate

of change in magnetic flux intersected by the coil and also with number of turns

e.m.f m / t and e.m.f N

So

-

m / t: change in magnetic flux with time, N: Number of turns of coil

6- Induced e.m.f in a straight wire

- when a wire of length L moves with velocity V normally on a regular magnetic field of density B

An induced e.m.f is produced in the wire

e.m.finduced = m / t = B t

Where is the change in the area the wire moved through

- if it moves a distance of x so L x

e.m.finduced = B L x / t

And x / t = V

e.m.finduced = B L V

- And if wire makes angle with field so

7- E.m.f generated by mutual induction

- When current intensity changes in the primary coil of rate 1 /t , and induced (e.m.f)2 is generated in

the secondary coil which is directly proportional with the rate of change in magnetic flux m /t

- So (e.m.f)2 m /t

- And m /t 1 /t

- Then (e.m.f)2 /t

- Where is the mutual induction coefficient

e.m.finduced = N m / t

e.m.finduced = B L V sin

(e.m.f)2 = /t

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8- E.m.f generated by self-induction

- Induced e.m.f produced is directly proportional with the time rate of change in magnetic flux so

e.m.f m /t

- The time rate of changing in magnetic flux is directly proportional with time range of changing in current

m /t /t

So e.m.f /t

e.m.f = - L /t

- Where Lis the self-induction coefficient

9- The induced instantaneous e.m.f. generated in Dynamo (Generator)

- When coil rotates with a linear velocity V, where the longitudinal ribs intersect the magnetic flux lines, so

if the angle between the direction of linear velocity and the plane of magnetic field is then induced e.m.f

generated in the each rib is

e.m.finduced = B L V sin

- And e.m.f in one turn (two ribs)

e.m.finduced = 2 B L V sin

V = distance / time = (circumference of circle for 1 rotation) / time for 1 rotation

V = 2 r / t and frequency f = 1 / t

V = 2 r f take 2 f =

V = r where is the angular velocity, r is radius of rotation and V is linear velocity

- e.m.finduced = 2 B L r sin

- We can take ( 2 r L = A ) where A is the Area of coil (L is the length and 2r is the width)

- e.m.finduced = B A sin

- And if coil has number of turns = N

- e.m.finduced = N A B sin

- = 2 = t =2 f t

= 2 f = t

e.m.finduced = N A B sin

e.m.finduced = N A B sin t

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10- Relations for the electrical transformer

A. Relation between the two e.m.f. of the two coils of ideal transformer and their number of turns

- When primary coil is connected to source and circuit of the secondary coil is open, an induced e.m.f is

generated in the primary coil by self-induction which is

- VP = NP m / t 1)

- When closing the secondary coil circuit, an induced e.m.f. is generated in the secondary coil by mutual

inductions because secondary coil intersects the flux lines of primary coil

- VS = NS m / t 2)

- We suppose there is no lose in magnetic flux then

Divide 2) by 1)

B. Relation between the two currents of the two coils of ideal transformer and their number of turns

- We suppose that there is no energy lose in the transformer so

Energy consumed in the primary coil in a specific time = energy generated in the secondary coil in the same

time

VP P t = VS S t

VP P = VS S

- Power input (primary coil) = Power output (secondary coil)

VS / VP = P /S

And VS / VP = NS / NP

This means that the current intensity in any coil is inversely proportional with its number of turns

VS / VP = NS / NP

P /S = NS / NP

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C. Factors that depends on

Physical quantity Factors that this quantity depends on

Induced e.m.f generated in a coil

1- Time in rate of change magnetic flux intersected by the coil 2- Number of turns

Induced e.m.f in a straight wire

1- Flux Density 2- Length of the wire 3- Velocity of wire intersecting to flux 4- Sin of angle between the wire and the field

Mutual coefficient between two coils

1- Permeability coefficient of medium 2- Volume of the coils (length and are of each turn) 3- Number of turns of the coils 4- The distance between them

Self-induction of a coil 5- Geometric shape of the coil 6- Number of turns 7- Length of the coil 8- Permeability coefficient of medium

The induced instantaneous e.m.f. generated in Dynamo (Generator)

1- Number of turns 2- Magnetic Flux Density 3- Area of the coil 4- Angular velocity that coil rotates with, or frequency of

rotation 5- Sin of angle between the coil and the normal plane of

the magnetic field

Consumed energy in a wire E = I V t 1- Current intensity 2- Potential difference 3- Time of current passage

e.m.finduced = N m / t

e.m.finduced = B L V sin

e.m.finduced = N A B sin t

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H. Comparisons

AC current DC current

How it’s obtained AC Generator - DC generators - Batteries and cells

Characteristics 1- it changes its value and direction with time

2- can be transferred for long distances without losing energy, by stepping up its voltage using transformers

3- can be converted to DC current

1- it’s constant in value and direction 2- cannot be transferred because it lose

its energy in form of heat 3- cannot be converted to AC current

Usage 1- Lighting 2- Heating 3- Operating machines

1- Lighting 2- Heating 3- Electrical plating 4- Charging batteries

Step-up Transformer Step-down Transformer

Usage Raising voltage at generating stations

Step-down voltage at consumption places

Number of turns NS > NP

NP > NS

Electromotive Force Vs > VP VP > VS

Current intensity IP > IS IS > IP

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Generator (Dynamo) Motor Transformer

Usage convert mechanical (motion) energy to electrical energy

A device used to convert electrical energy to mechanical (motion) energy

1- step up or step down the alternating voltage

2- reduce losing energy during its transfer from generators to consumption places through far distances

3- In some home devices

Structure Rectangular coil of copper wire rolled around core of wrought iron, the coil and core can be rotated easily and placed inside a magnetic field

Rectangular coil of copper wire rolled around core of wrought iron, the coil and core can be rotated easily and placed inside a magnetic field

Two coils (primary, secondary) are rolled around a core of wrought iron formed of insulated slices to avoid eddy currents

Operation Terminals of coil are connected to two split rings rotate with the coil and each ring touches a fixed graphite brush which connect the induced current of coil to external circuit

Terminals of coil are connected to two halves of a cracked cylinder, each half is connected to a fixed graphite brush, these brushes are connected to DC source (Cell)

Primary coil is connected to the source of AC current needed to raise or reduce its voltage VP

and secondary coil is connected to the external circuit that needs a specific value of voltage Vsf

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D. Experiments

Experiment 1 Faraday’s Experiment

OR

- Experiment to generate induced current in a coil

OR

- Experiment to convert mechanical energy to electrical energy

Steps and Notices

1- Connect terminals of coil of copper wire to a sensitive galvanometer which has zero in middle grade

2- Place a magnet inside the coil

Notice

- Galvanometer pointer moves in a specific direction

3- Pull the magnet outside the coil

Notice

- Galvanometer pointer moves in opposite direction

4- Fix the magnet and move the coil near and far the magnet

Notice

- Galvanometer pointer moves in the two directions according to movement of the coil

Deduction - Results

An induced e.m.f and induced current is generated in a coil as a result of changing the magnetic flux around this

coil (when intersecting the magnetic lines by the coil), the direction of this induced current depends on the

movement direction of the magnet near or far the coil

- Experiment 2 Mutual induction between two coils

Steps and Notices

1- Connect a coil to a circuit has (battery ,key and rheostat) to be the primary coil and connect another coil

(secondary coil) to a galvanometer has zero in its middle graduation

2- Close the circuit of the primary coil and move it near to secondary coil

Notice

- Galvanometer pointer moves in a specific direction

3- Move the primary coil far away the secondary coil

Notice

- Galvanometer pointer moves in opposite direction

4- Fix the primary coil inside the secondary coil and increase current intensity in the primary coil

Notice

- Galvanometer pointer moves in a specific direction

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5- Decrease current intensity in the primary coil

Notice

- Galvanometer pointer moves in opposite direction

Deduction

We can generate induced e.m.f and induced current in a secondary coil by effect of a primary coil where

- Reverse induced e.m.f and reverse induced current : by increasing the magnetic field of primary coil so the

induced current in the secondary coil is in direction to oppose the change causing it (in the primary coil) to

resist the increase of magnetic field

- Directed induced e.m.f and directed induced current : by decreasing the he magnetic field of primary coil so

the induced current in the secondary coil is in direction to oppose the change causing it (in the primary coil)

to resist the decrease in the magnetic field

-

Experiment 3: self- induction

Steps and Notices

1- connect a coil of a strong magnet (of high number of turns) in series with (a battery of 6 volts, key) and in

parallel with a lamp which works under voltage of 180 v

2- close the circuit

Notice

- Lamp doesn’t work

3- Open the circuit Notice

- An electrical spark between the terminals of the key and lamp is lightening for a very short time

Deduction

1- When closing the circuit a reverse induced e.m.f and a reverse induced current is generated in the coil which

delays the main current to reach its max. value and a strong magnetic field is generated in the coil because each

turn is considered a small magnet

2- When opening the circuit the current is attenuated يضمحل (decreases) so an induced e.m.f and induced current

is generated in the coil by self-induction this induced e.m.f is high because number of turns is big and the time

rate of changing the current is also big e.m.f /t and induced current is high so it generates an electrical

spark

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E. Some Explanations 1- Specifying the direction of induced current using Lenz’s rule:

- When moving the north pole of a magnet near to a coil which has a current passes through it, the face of the

coil which is near to the magnet will be also a north pole and an induced current will pass through the coil in

the anti-clockwise direction to resist the change causing it N N

- When moving the north pole of a magnet far from a coil which has a current passes through it, the face of

the coil which is near to the magnet will be a south pole and an induced current will pass through the coil in

a clock-wise direction to resist the change causing it N S

2- Fleming’s Right Hand Rule

Usage:

- Specifying the direction of induced current passing in a straight wire which moves perpendicular to a

magnetic field

How it’s used

- make the thumb, index (forefront) and middle fingers are perpendicular, so

- Thumb: refers to direction of movement

- Index (forefront) : refers to magnetic field

- Middle: refers to the induced current direction

3- Eddy currents disadvantages and how to avoid them : - Disadvantages: large part of electrical current is lost in thermal energy

- How to avoid them? Made the iron core from thin insulated slices of silicon-wrought iron which has high

resistivity

4- Transformer Operation: - The primary coil is connected to an AC source (needed to be transformed) and the secondary coil is

connected to the external circuit which will use the transformed current

- When closing the circuit of the secondary coil and AC current passes through the primary coil, an alternating

magnetic field is generated and the iron core will collect and concentrate it in the secondary coil turns

- An induced e.m.f and induced current is generated in the secondary coil which is larger or less than the

source according to the ratio between number of turns in both coils

5- How does Motor works along complete cycle

- In the first half cycle

When the coil is parallel to the magnetic field its terminals (the two halves of cracked cylinder) touch the

graphite brushes, so current will pass through coil and two opposite forces acting on two ribs so they produce a

torque causing rotation for the coil

Torque decreases gradually with the rotation of the coil until it vanishes when its plane is perpendicular to

magnetic flux, but the coil continue rotating according to inertia until it returns back to its original position

(parallel to the field)

- In the second half cycle

Coil is parallel to the field so torque will be generated in the same direction so coil will continue rotation in the

same direction

Torque decreases gradually until it vanishes , but the coil continue rotating according to inertia until it returns

back to its original position (parallel to the field) this will happen each cycle

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Current flows in the same direction in two parallel wires

F. What Happens in these cases 1- Moving a coil has electrical current near to another coil connected to a galvanometer

- A reverse induced e.m.f is generated in the second coil by the mutual induction

2- Open an electrical circuit contains a magnetic coil connected in parallel with a battery

- An electrical spark happens across the key terminals

3- Open the primary coil circuit when it’s inside the secondary coil

- A direct induced e.m.f. is generates in the secondary coil to resist the shortage in the primary coil current

4- Increasing value of current in the primary coil placed inside a secondary coil which is connected to a

galvanometer

- Galvanometer pointer deflects in one directions because of generating reverse induced e.m.f. on the

secondary coil by mutual induction

5- A high frequency current passes through a coil rolled around a piece of metal

- Its temperature will increase according to eddy currents

6- Growth of current in a coil rolled on a wrought iron core inside it to the time of current growth

- The time of current growth will increase in the coil as a result of generating a big reverse induced e.m.f

because permeability coefficient of wrought iron is high and self-induction coefficient of it will be also high

7- Wires of electrical resistance are doubled rolled

- Self-induction will vanish so the main current will be only affected by Ohmic resistance, because the

magnetic field produced by on turn will cancel the magnetic field produced by the next turn

8- Increasing number of turns of dynamo to double and number of cycles in 1 second to double

- Induced e.m.f. will increase 4-times

9- Increasing number of turns of Dynamo coil to double and decreasing its angular velocity 4 times

- Instantaneous induced e.m.f. will be reduced to half

10- Replacing the two split rings of Dynamo with cylinder cracked to 2 halves

- AC current will be converted to unified direction current of alternating values

11- Dividing the cracked cylinder in Dynamo to number of pieces equal double number of coils

- This will completely convert the AC current to DC current which is unified in direction and constant value

12- Connecting primary coil in a transformer with a cell (battery)

- The magnetic flux resulting on it will be constant so, no mutual induction will happen between the coils and

the transformer will not work

13- Opening circuit of secondary coil in the transformer and connecting its primary coil with an AC source

- A reverse induced e.m.f. is generated in the primary coil, it’s equal to e.m.f. source so current is approximately

zero

14- Transferring AC current for long distances without raising voltage before transfer

- A lot of energy is lost in the wires in form of thermal energy

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Give reason

1- An induced e.m.f. is generated in a wire moves normally on magnetic flux lines

- Because the magnetic flux affects the free electrons of the moving wire so these electrons will release from

one terminal of the wire(+ve terminal) to another terminal (-ve terminal) so a potential difference is

produced between the two terminals of wire

2- Induced e.m.f may not be generated in a moving wire in a magnetic field

- Because the direction of wire movement is parallel to the magnetic flux lines, so according to law

e.m.finduced = B L V sin angle between field and wire will be 0 and e.m.f. will be zero

3- Induced e.m.f. produced in a coil is higher if the core of the coil is made of wrought iron

- As the wrought iron has a higher permeability coefficient and this will increase concentration of magnetic

flux lines that are intersected by the coil which leads to increase the induced e.m.f

4- Wires of standard resistance are double rolled

- To avoid the self-induction because the magnetic field produced by a turn is cancelled by the magnetic field

produced by the next turn, so current will only affected by the Ohmic resistance

5- A piece of wrought iron doesn’t magnetized if it’s caught by double rolled wire has a current passing through

it

- Because the direction of current in the first wire opposes the direction of current in the second wire so

magnetic field generated by one of them will cancel the other, so resultant magnetic field equals zero

6- The direct e.m.f. induced in a coil by self-induction always bigger than the reverse induced e.m.f

- Because the collapse rate of current is always bigger than the growth rate of current

7- Current intensity doesn’t reach maximum value in coil in the moment closing the circuit, and doesn’t vanish

also in the moment of opening the circuit, it takes time

- This happens because of generating a reverse e.m.f. in the moment of closing and opening the circuit this

reverse e.m.f will oppose the main current whether when it increases or when it decreases

8- Current is growing in a straight wire faster than a coil

- Because the magnetic field produced around the wire is not intersected by the wire itself so there is no

reverse induced current produced in it, but in case of coil the magnetic field produced in coil is intersected

by the coil itself so a reverse induced e.m.f is generated in coil by self-induction and also a reverse induced

current so it resist the main current in the coil

9- Vanishing the induced current in a straight wire is faster than it in a coil of air core which is faster than it in a

coil rolled on an iron core

- There is no reverse induced e.m.f generates in the wire because the wire doesn’t intersect its magnetic field

- In the coil of air core, there is a reverse induced current is generated in coil to oppose the shortage in

current its value is high

- In the coil of iron core, the reverse induced current is higher because the magnetic field is bigger than it in

the coil of air core according to the permeability coefficient

10- When opening circuit of electrical magnet there is a spark appears in the position of cutting the current

- Because the rate of vanishing the current is very high so the rate of changing the magnetic flux is very high

which leads to generating high induced current in the same direction of the main current to oppose its

shortage

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11- When AC current passes in a coil rolled on a piece of metal its temperature increases

- Because of the eddy currents produced in it which leads to melt the metal

12- Eddy currents don’t produced in a fixed piece of metal otherwise the magnetic field around it is variable

- As in the variable magnetic field, the magnetic flux lines intersected by the metal is changing so eddy

currents are generated

13- Temperature of an iron cylinder is raised if it’s rolled by a coil connected to AC source

- As the AC current changes its value and direction periodically, so the magnetic field resulting by it is also

changing, so eddy currents are produced in the cylinder

14- Induced e.m.f in the Dynamo (generator) coil is max. value when its plane is parallel to the magnetic field

- According to this relation

e.m.finduced = N A B sin

is the angle between the coil and the normal plane to the magnetic field so in this case equals 90 so

Value of e.m.f will be maximum = N A B

15- E.m.f (average) in Dynamo through ¼ cycle = E.m.f (average) in Dynamo through ½ cycle

e.m.finduced = N m / t

In ¼ cycle:

m = BA , t = ¼ T

e.m.f = 4 N B A F In ½ cycle:

m = 2 BA , t = ½ T

e.m.f = 4 N B A F 16- E.m.f (average) in Dynamo coil through a complete cycle = 0

- As the average value of e.m.f in one direction( ½ cycle) is equal to average value of e.m.f in the opposite

direction (in the second ½ cycle) so the resultant equal zero

17- the cracked cylinder in dynamo produce a unified direction current

- when coil is rotated in half cycle their terminals rotate with it and the current will pass in the same direction

in the external circuit when touching the graphite brushes

18- Terminals of Dynamo coils are connected to number of cracked pieces which is double number of coils

- To guarantee that brushes are always touched to the coil which is parallel to the magnetic field to finally

produce a current of constant value DC current

19- The core of transformer is made of slices of wrought iron which are insulated

- Permeability coefficient of wrought iron is high so it helps in concentrating the magnetic flux lines

- Resistivity of wrought iron is high and when it’s made of insulated slices, this will increase its resistance to

resist the eddy currents and reduce the energy loss in form of heat

20- In Ammeter or Galvanometer the iron core is NOT divided into insulated slices

- Because Ammeter and Galvanometer used to measure dc currents, so there is no eddy currents are

produced in the core , no change is happened in the magnetic flux

21- Transformer coils are made of copper wires

- Because its resistivity is very low so the coils resistance is very low which avoid energy loss in form of heat

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22- There is no transformer with 100% efficiency

- Because there is energy loss in forms of:

A. Loss in magnetic flux lines from primary coil to secondary coil

B. Loss in heat through the wires

C. Mechanical energy according to the movement of the iron core magnetic molecules

23- Transformers are not used in step-up or step-down a DC e.m.f.

Or Transformers don’t work if the primary coil is connected to DC source

- Because the magnetic flux produced by the DC current is constant so no induced e.m.f is produced in the

secondary coil by mutual induction (there is no mutual induction happens)

24- Transformer doesn’t consume power when opening circuit of secondary coil, although its primary coil is

connected to electrical source

- When opening the secondary coil circuit a reverse induced e.m.f. is produced in the primary coil (by self-

induction) and it’s equal to e.m.f (source) so there is not potential difference and there is no current passes

in the primary coil and no power is consumed

25- Transformer works when closing its secondary coil circuit

- When closing secondary coil circuit, current passes through it, the magnetic flux resulting by it will be

intersected by the primary coil and it vanishes the reverse induced current in it, so the current of source will

pass through the primary coil and continue working

26- Electrical energy is transferred from generators stations to consumers under a high voltage and low current

- To reduce the consumed energy in the wires because power is directly proportional with square of current

intensity

27- Use of step-up transformers at the generating stations

- Because the step-up transformers raise the voltage at the generating stations which leads to reducing the

current intensity in the transformer and this is useful in avoiding loss in energy consumed in transferring

wires

28- The step-up transformers are current step-down and vice versa

- Because the power is constant and this makes the voltage inversely proportional with current

V = Pw/ I

29- Motor continue in rotation although it passes through the position which is normal to magnetic field

Or

The coil of electrical motor doesn’t stop when the graphite brushes touches the insulation part of the cracked

cylinder halves

- Because the inertia makes the coil to continue rotating and the two halves exchange their positions and also

current exchange its direction so torque will be in the same direction

30- To increase Motor power, we use several coils separated by small angles

- To increase the torque by guarantee that the coil is always parallel to the magnetic flux so the torque is

always maximum value an coils rotates with high angular velocity, this leads to enhance the motor efficiency

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Laws

E.m.f in Dynamo (Generator)

A. Instantaneous e.m.f. e.m.f = e.m.fmax. Sin

e.m.f = N A B sin t

V / r = t = 2T = 2 f

inside (sin) = 180

outside (sin) = 22/7

B. Maximum e.m.f. E.m.f max. = N A B

C. Effective e.m.f.

E.m.f effective = e.m.fmax. Sin 45

D. Average e.m.f.

In ¼ cycle and ½ cycle

e.m.f = 4 N B A F

In ¾ cycle

e.m.f = 4/3 N B A F

In 1 cycle

e.m.f = 0

Instantaneous induced current

Instantaneous = IMAX sin

Number of reaching the AC current to maximum value

in 1 second= 2 f

Number of reaching the AC current to zero in 1 second

= 2 f +1

Laws

Faraday’s Law

e.m.finduced = N m / t

- If area changed

e.m.finduced = N B / t

- If flux density changed

e.m.finduced = N B / t

- If coil rotates

A. ¼ cycle (90)

e.m.finduced = N B / t

B. ½ cycle (180)

e.m.finduced = 2 N B / t

C. 1 complete cycle

e.m.finduced = because m=0

E.m.f. induced in a coil

Self-induction:

e.m.f = - L /t = N m / t

(Self-induction coefficient)

L = / L (length)

Mutual Induction

(e.m.f) 2 = /t = N2 (m )2/ t

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Laws

Electrical Transformer

A. Ideal Transformer:

VP P t = VS S t

VS / VP = P /S

P /S = NS / NP

In case of 2 secondary coils:

(Pw) p = (Pw) s1 + (Pw) s2

B. Non-Ideal Transformer:

ɳ = (Vs Is/VP Ip) * 100

ɳ = (Vs Np/Vp Ns) * 100

(Pw) p > (Pw) s

Pw (consumer) = Pw (station) - Pw (loss in wires)

1- Power at generating stations = I V

2- Power consumed in wires = I2 R

3- Shortage in Volt = I R

Laws

Electrical Motor

A. Current Intensity

- Before operation

I = e.m.f. (source)/ R

- During Running

I = e.m.f. (motor)/ R

B. Electromotive force

E.m.f motor = e.m.fsource – e.m.freverse

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Chapter 4

X. Definitions 1- AC current

- It’s the current that changes its magnitude gradually from 0 to maximum after quarter cycle and

changes its direction after half cycle

2- AC frequency :

- It’s the number of complete cycles of AC current in 1 second

3- Periodic Time of AC:

- It’s the time taken by AC current to make a complete cycle

4- Hot Wire Ammeter:

- Device used to measure AC or DC current and it depends on the expansion of a wire made of alloy of

platinum and iridium by the thermal effect of electrical current

5- Inductive Reactance:

- It’s the resistance of a coil caused by its self-induction Xl

6- Electrical Capacitor:

- Two parallel insulated metal plates, used to store electrical energy in form of electrical field

7- Capacitance:

- The ratio between the charge placed on one plate and the potential difference between the two plates

8- Capacitive Reactance:

- It’s the resistance of a capacitor caused by its capacitance Xc

9- Farad:

- It’s the capacitance of a capacitor that ,if it’s charged by a charge of 1 coulomb the potential difference

between its plates is 1 volt

10- Impedance:

- It’s the equivalent for the ohmic resistance, inductive reactance and the capacitive reactance for an AC

circuit

11- Oscillator Circuit:

- It’s an electrical circuit in which there is an exchange for energy stored in inductive coil in form of

magnetic field and the energy stored in a capacitor in form of electrical field

12- Resonant Circuit :

- It’s an oscillator circuit contains a resistance, inductive coil, capacitor and AC source and it only allows

passage of AC current has frequency equal or very close to its frequency

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Y. What’s meant by 1- AC frequency is 50 Hz

- it means that number of complete cycles that made by AC current in one second is 50 cycles

2- Periodic Time of AC current is 0.02 second

- This means that time taken by AC current to complete 1 cycle is 0.02 second

3- Inductive reactance of coil is 100 ohm

- It means that the resistance for the coil resulting in its self-induction is 100 ohm

4- Capacitance for a capacitor is 5 micro-farad

- It means that the quantity of charges placed on one plate is 5 *10-6 coulombs when the potential

difference between is plates is 1 volt

5- Capacitive reactance is 100 ohm

- It means that the resistance of the capacitor according to its capacity is 100 ohm

6- Impedance is 50 ohm

- it means that the equivalent resistance for (ohmic resistance. Inductive reactance, capacitive reactance)

is 50 ohm

7- Phase angle for a circuit has inductive coil and resistance is 45o

- It means that the total voltage leads current by angle 45o

Tan = VL/VR = XL/R = 1 , XL =R, VL=VR

8- Phase angle for a circuit has capacitor and resistance is 45o

- It means that the total voltage lags current by angle 45o

- Tan = - VC/VR = -XC/R = - 1 , XC =R, VC=VR

9- Resonant circuit frequency is 104 Hz

- It means that the oscillator circuit frequency equals source frequency = 104 Hz and it only allows the

current of this frequency to pass through it and inductive reactance equals the capacitive reactance only

at frequency 104 Hz

Z. Devices

Device Usage Scientific Idea and explanation

1- Hot Wire Ammeter Measures the effective value of AC current and it also measures DC current

Idea: Thermal effect of electrical current Explanation: When current (DC or AC) passes through an ohmic resistance it generates a quantity of heat which depends on the effective value of this current

2- Antennas

Radio channels Idea: Resonance circuit Explanation:

When we change the channel on radio device, the frequency of the resonance circuit changes to a specific value which equals the frequency of the desired channel current (because electromagnetic wave of the channel is converted to AC current)

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AA. Usages

1- Platinum-Iridium Wire It’s heated up and expands when electrical current passes

through it so we can measure the effective value of current

2- Silk thread in Hot-Wire Ammeter It is pulled by the platinum-iridium wire so the roller will rotates and pointer will move and stops on the effective value of the current

3- The board on which the platinum wire is tensed

Get rid of zero error

4- Roller in Hot-Wire Ammeter It rotates when it’s pulled by the silk thread, so pointer will deviate until it reaches the effective value

5- Coil in Hot-Wire Ammeter It pulls the silk wire to rotate the roller and move the pointer to the effective value of the current

6- The resistance connected to the platinum-Iridium wire

It divides the total current to allow a suitable current to pass through the wire

7- The variable-capacity capacitor in RLC circuit which works as resonant circuit

when changing the capacitor capacitance its capacitive reactance will change until it equals the inductive reactance of coil which means that the impedance will equal the ohmic resistance only (minimum impedance) and current will be maximum value (it’s used in receiver devices)

8- Resonance Circuit Used in receivers to receive a specific wave

BB. Figures

CC. Deductions 1- Frequency of current in resonant circuit

- In resonant circuit, current will be maximum when inductive reactance equal capacitive reactance

- XL= XC

- 2fL = 1 / 2fC

- f 2=1/4LC

f = 1/2√ LC

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DD. Factors dependent on :

4- Angle of deviation in Hot-Wire Ammeter - Square of current intensity

5- Inductive reactance of a coil XL= 2 f L 4- Self-induction coefficient 5- Frequency of current

6- Capacitive Reactance of a capacitor XC= 1/ 2 f C 1- Capacity of capacitor 2- Frequency of current

7- Total impedance Z = √ R2+(XL-XC)2 1- Ohmic Resistance 2- Inductive reactance 3- Capacitive reactance

8- Frequency of resonant circuit f = 1/2√ LC 1- Square root of capacity 2- Square root of self-induction coefficient

I. Comparisons

Hot-Wire Ammeter Moving Coil Ammeter

Idea Of Work Expansion resulting on thermal effect of electrical current

Torque resulting on the magnetic effect of electrical current

Usage Measuring intensity of DC current and effective value of AC current

Measuring DC current only

Scale (graduation) Non-regular Regular

Effect of room temperature

It’s affected by room temperature It doesn’t affected

Pointer move It moves slowly when passing the current or cut-off

It moves faster when passing the current or cut-off the current

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Circuit of R and XL (RL) circuit

Circuit of R and XC

(RC) circuit Circuit of XL, XC,R (RCL) Circuit

Resonant Circuit

Circuit

Total Voltage V = √ VR2+ VL

2

V = √ VR2+ VC

2

V = √ VR2+ (VL- VC)2

VL=VC V = VR

Impedance Z = √ R2+XL2

Z = √ R2+XC

2

Z = √ R2+(Xl-XC)2

XL= XC

Z = R

Phase Angle Tan = VL/VR = XL/XR

is Positive

Tan = - VC/VR

= -XC/XR

is Negative

Tan = (VL-VC) / VR

=(XL-XC)/R

When XL> XC is Positive

When XL< XC is Negative

Tan = 0

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J. Important Explanations

1- Disadvantages of Hot-Wire Ammeter

A. Its pointer moves slowly until stop at effective value and also it returns back to zero slowly B. Platinum-Iridium wire is affected by the room temperature which causes some errors in readings

called zero error 2- AC circuit contains non-inductive resistance

A. V = Vmax. sin ω t B. I = V / R So I = Imax. sin ω t C. From A. and B. we found that in this circuit voltage and current are in phase it means they reach 0

together and maximum value together

3- AC circuit contains an inductive (non-resistive) coil

A. When closing the circuit, voltage between terminals of coil reaches Vmax. ,current grows gradually and voltage decreases gradually according to the reverse induced e.m.f. until current reaches maximum at the moment in which voltage is zero

B. Induced current is generated in the coil and it resist the change causing it this is the cause of lag1-ging current in reaching maximum with voltage

C. Vinduced = - L /t D. Current lags يتأخر عن voltage by 90o or ¼ cycle E. XL = 2πfL

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4- AC circuit contains a capacitor

A. In 1st quarter, current reaches maximum, where –ve charges are transferred on plate A and its potential is

decreased, these charges affect plate B and repulsed with –ve charges on plate B so plate B has only +ve charges, at this moment capacitor is charged and current stops (equal 0)because voltage on capacitor = voltage of source = maximum value

B. In 2nd quarter e.m.f.source decreases so potential difference across the capacitor is higher than source so it discharges in source, current will reach maximum and voltage of capacitor reaches 0

C. In 3rd quarter, capacitor will charge again but in the opposite direction (plate B is –ve and Plate A is +ve) until its voltage reaches e.m.f.source so current stops =0 and voltage is maximum

D. In 4th quarter, capacitor discharges and its voltage will be 0 and current is maximum

I = C V/t E. Current leads يسبق voltage by 90o or ¼ cycle F. XC= 1 / 2πfC

5- RL Circuit

A. In the coil V leads by 90o or ¼ cycle

B. In Ohmic resistance V and are in phase C. Current is the same because they are connected in series D. Voltage of coil leads voltage of resistance by 90o E. V = √ VR

2+ VL2

F. Z = √ R2+XL2

6- RC Circuit

A. In capacitor V lags by 90o or ¼ cycle

B. In Ohmic resistance V and are in phase C. Current is the same because they are connected in series D. Voltage of resistance leads voltage of capacitor by 90o

E. V = √ VR2+ VC

2

F. Z = √ R2+XC2

7- RCL circuit

A. In the coil V leads by 90o or ¼ cycle

B. In Ohmic resistance V and are in phase

C. In capacitor V lags by 90o or ¼ cycle

D. Current is the same because they are connected in series E. V = √ VR

2+ (VL- VC)2

F. Z = √ R2+(Xl-XC)2

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8- Oscillator Circuit A. Structure

I. Inductive coil of a very small resistance II. Capacitor

III. Battery and all are connected in parallel B. Operation

I. When close key “A” - Current passes in the capacitor - One plate (connected to positive pole) is charged with

positive charge, and the other plate is charged with negative charge

- Current stops when potential difference across capacitor is equal to VBattery1

- Energy is stored in capacitor in form of electrical field - Open key “A” ,now capacitor is charged

II. When closing key “B”

- Capacitor discharges through coil and current flows from the positive plate to negative plate, potential difference between plates will decrease until it vanishes and the electrical field disappears

- The coil stores energy in form of magnetic field resulting on the current passes through it - In the beginning, the potential difference through capacitor is high so current passing through the coil is

high, after an interval of time P.D. in capacitor decreases and current also decreases in the coil - This shortage in current leads to generate a direct induced e.m.f in the coil by its self-induction, this

induced e.m.f. attracts positive charges from the positive plate to negative plate, so positive plate will be charged with negative charges and negative plate will be charged with positive charges

- Capacitor is now charged in opposite direction and this means that magnetic energy is converted again to electrical energy

- Capacitor will start discharging in opposite direction in the coil and electrical field is converted to a magnetic field and so on , which causes many oscillations in the circuit according to this exchange

9- Relation between frequency and (XL XC R Z)

- Impedance Z decreases until it reaches minimum Z =R when XL=XC and it increases with frequency - Current increases with frequency until it reaches maximum when XL=XC then it decreases with frequency

increase, this is because current is inversely proportional with impedance - Circuit is resonant (in resonance state) when XL=XC

f = 1/2√ LC

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G. What Happens in these cases 1- Flow of AC current in an Ohm resistance to its temperature

- Its temperature increases because of energy loss in form of thermal energy

2- AC or DC current pass through the Hot-Wire Ammeter

- Thermal energy is generated in the Platinum-Iridium wire so it expands and allows to the silk thread to

make the roller to rotate and pointer to deviate so it gives the value of effective current

3- Cutting-off current passes in Hot-Wire Ammeter

- The wire is cooled and attracts the silk thread which rotate the roller to returns the pointer to zero

4- The silk thread is cut

- The expansion of platinum-iridium wire will not affect the roller or the pointer so, Ammeter will not give

a reading

5- Passage of AC current in an inductive coil to the phase angle between current and voltage

- Voltage leads current by 90O or ¼ cycle

6- if frequency of AC current is highly increased

- the inductive reactance will increases also by relation XL= 2 f L until it prevents the flow of current

7- Capacitor is connected to DC source

- Current flows in the circuit in a small interval of time then it decreases until it vanished when P.D. of

capacitor = VBattery

8- Passage of AC current in a circuit contains capacitor to the phase angle between current and volt

- Current leads voltage by 90O or ¼ cycle

9- High Increase of frequency of electrical current passes through a capacitor

- Capacitive reactance will decrease according to relation XC= 1/ 2 f C and circuit is considered short-

circuit

10- Connecting a resistance with an inductive coil and AC source to the phase angle between current and

total voltage

- Voltage leads current by angle where tan = VL / VR = XL / R

11- Connecting a resistance with an inductive coil and AC source to the phase angle between current and

total voltage

- Current leads voltage by angle where tan = - VC/ VR = - XC / R

12- Connecting a charged capacitor to inductive coil

- Capacitor discharges in the coil and an instantaneous current flows ,so a reverse induced e.m.f. is

generated in the coil in opposite direction of the main current, this operation is reversed several times

causing oscillations so it’s called Oscillator circuit

13- The inductive reactance equals the capacitive reactance in RCL circuit

- The circuit is resonant, and total impedance is minimum (Z =R) and current is maximum , voltage and

current are in phase = 0 and frequency f = 1/2√ LC

14- Replacing AC source with DC source of the same effective value in RL circuit to the current intensity

- Current will increase because total impedance is decreased when AC source is replaced by DC source

- In case of AC : current has frequency f and coil has inductive reactance XL= 2fL so Z is high Z = √ R2+XL2

- In case of DC : frequency =0 and XL=0 so Z is low Z = R only , current will increase

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K. Give reason 31- Hot-Wire Ammeter is used to measure AC and DC currents

- As it generally depends on the thermal effect of any electrical current, it measures the effective value of

current according to the expansion of Iridium-Platinum wire by heat caused by current passage in the

wire.

32- An alloy of Platinum-Iridium used in the Hot-Wire Ammeter

- As it expands easily by heat when current flows through it

33- Platinum-Iridium wire is connected in parallel with a resistance R

- To work as a shunt resistance (it divides the current) to allow a suitable part of current to pass through

the wire

34- Hot-Wire Ammeter is connected in series in the electrical circuit

- To measure the current needed to be measured not part of it

35- Hot-Wire Ammeter divisions are not regular

- Because the quantity of heat generated in the wire is directly proportional with the square of effective

current not the current only

36- There is an error in Hot-Wire Ammeter called zero error

- Because the platinum-iridium wire is affected by the room temperature

37- The platinum-iridium wire is tensed on a board made of a material has the same expansion coefficient of

the wire and insulated from it

- To overcome the error caused by affecting the wire by the room temperature

38- Current and Volt are in phase in ohmic resistance circuit

- Because V = Vmax sin t and = V / R , = (Vmax sin t) / R

So = max sin t

They have the same phase angle so they vanishes together and reaches maximum together

39- At very high frequencies AC current may not pass through the inductive coil

- Because inductive reactance is very high XL= 2 f L and circuit is considered open circuit

40- Passage of AC in an inductive coil (non-resistive) don’t loss energy

- Because the only existent resistance is the inductive reactance that results in generating reversed

induced e.m.f in the coil so it maintains the energy in form of magnetic field

41- When increasing number of turns for a coil the inductive reactance increases if AC current of a constant

frequency passes

- Because inductive reactance XL is directly proportional with self-induction coefficient L when the

frequency is constant XL= 2 f L

And self- induction is directly proportional with square of number of turns L = µ N2 A / L (length)

42- Inductive reactance increases when put wrought iron core inside the coil and passing the same AC current

- Because inductive reactance XL is directly proportional with self-induction coefficient L when the

frequency is constant XL= 2 f L

- And self- induction is directly proportional with permeability coefficient L = µ N2 A / L (length)

- And permeability coefficient of wrought iron is higher than Air

43- When connecting group of inductive coils in parallel, the resultant inductive reactance is lower than the

smallest one

- Because the reciprocal of the resultant inductive reactance is equal to the sum of the reciprocal of all of

them (1/XL = 1/XL1+1/XL2 +1/XL3 +…….)

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44- When connecting a capacitor with DC source, current flows in a short time then it vanishes

- Current passes from battery to capacitor and +ve charges are placed on one plate and negative charges

placed on the other plate so a reverse potential difference is generated on the capacitor and increases

with time and current decreases until Vcapacitor = VBattery , at this moment current stops because there is no

difference in potential between battery and capacitor

45- The capacitive reactance doesn’t cause loss in energy

- Because capacitor store electrical energy in form of electrical field

46- When an AC current of high frequency passes through a capacitor, the circuit is considered closed circuit

- Because XC= 1/ 2 f C , this means that the capacitive reactance is inversely proportional with frequency

so at high frequency the capacitive reactance is very low and current passes in a closed circuit(no

resistance)

47- When connecting a group of capacitors in parallel the capacitive reactance for the group is less than the

lowest capacitive reactance for each capacitor

Because the total capacitance of a group connected in parallel equals the summation of them

(CT = C1 + C2+ C3+ ….) so it will be higher than any of them, and the capacitive reactance is inversely

proportional with the capacitance XC= 1/ 2 f C

48- The inductive reactance of a coil passes through it a dc current equals 0

- Because DC current is unified in magnitude and direction so its frequency equals 0 and inductive

reactance XL= 2 f L so it will be XL= 0

49- It’s impossible to produce an inductive coil of resistance zero

- Because any coil made of conducting wires which should have a little value of resistance according to its

resistivity

50- If an inductive coil has ohmic resistance is connected to AC source, the total voltage leads current by angle

where 0 < < 90

- Because current and volt are in phase in the ohmc resistance and volt leads current by angle of 900 in

the coil so the total voltage leads current by angle tan = VL / VR

51- If a capacitor is connected to an ohmic resistance and AC source of high frequency in series, the current

will lead the total voltage by angle where 0 < < 90

- Because voltage and current are in phase in the resistance and current leads voltage by angle of 900 in

the capacitor so the current will lead the total voltage by angle where tan = - VC / VR

52- In Oscillator circuit, the process of charging/discharging stops after an interval of time

- Because a part of electrical energy is converted gradually to thermal energy consumed in wires

according to its resistance so after time , AC current decreases and P.D. across capacitor also decreases

until it vanishes

53- To continue in charging/discharging process we should feed the capacitor with additional charges after

intervals of time

- To overcome energy loss as heat according to wires resistance

54- Ohmic resistance has a constant value regardless the value of frequency but inductive reactance and

capacitive reactance changes with frequency

- Because ohmic resistance doesn’t depend on the frequency but inductive reactance and capacitive

reactance depend on frequency according to these relations

- XC= 1/ 2 f C

- XL= 2 f L

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-

55- Capacitor allows the AC current to pass through its circuit

- When AC current passes, the capacitor is charged in the 1st quarter until voltage of it is equal to VSource

then e.m.f of source decreases in the 2nd quarter so VCapacitor > VSource so capacitor will discharge in the

source but source continue in decreasing its e.m.f until it reaches zero at the moment in which VSource

also reached zero and this process is repeated in the 3rd and 4th quarter but in the opposite direction

56- In resonance state current intensity is maximum

OR

In resonance state the current and total voltage are in phase

- Because the inductive reactance is equal to capacitive reactance so the total impedance Z = R so the

current is maximum value because resistance is minimum value and the voltage and current are in same

phase according to these relations

- V = Vmax sin t and = V / R , = (Vmax sin t) / R

So = max sin t

57- The average of electrical power consumed in a complete cycle of AC current in an inductive coil is 0

- Because coil stores energy in the 1st quarter in form of magnetic field and discharges it in the 2nd

quarter and repeats this in the second half(3rd and 4th quarters ) so after 1 cycle the total power =0

58- The average of electrical power consumed in a complete cycle of AC current in a resistance is not 0

- Because current needs work to transfer charges in both directions and this work doesn’t depend on the

direction of the current

59- We don’t sum the voltages in RCL circuit to get the total voltage

- Because each volt has a specific direction so we deals with them as vectors - V = √ VR

2+ (VL- VC)2

60- When replacing DC voltage source by an AC voltage source of the same effective e.m.f. in RL circuit, the

impedance increases

- Because an inductive reactance is generated in the coil according to its self-induction which wasn’t exist

in case of DC because frequency was zero ,

- It was Z = R and became Z = √ R2+XL2

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AC and DC current Comparison

Hot Wire Ammeter

Used to measure the effective value of AC

Construction:

1- Thin wire of (platinum-Iridium) alloy, this wire is stretched between terminals of the device, so when it heated

up it will expand

2- One end of silk thread attached to the middle of the wire, the other end rolled over a roller which is fixed on a

spring to the wall

3- A pointer is attached to roller and moves over a scale

4- The alloyed wire is connected with a shunt resistance in parallel

Direct Current DC

1- It’s a constant value current that

flows from +ve pole to –ve pole of a

battery (conventional direction)

2- Its sources are (cells, batteries and

DC generators)

3- Its e.m.f cannot be raised or

reduced

4- Measured by moving coil

Galvanometer or Ammeter

5- Used in electrolysis, electroplating

and Batteries charging

6- Transferred, but with a big loss of

energy

Alternative Current AC

1- It’s a current that changes its value

from zero to maximum each quarter

cycle and changes its direction each

half cycle

2- Its source is AC generators

3- Its e.m.f increases and decreases

using transformers

4- Measured by the Hot wire Ammeter

which measures its effective value

5- Used in most electrical devices and

lightening

6- Transferred with minimal loss of

energy

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Operation of Hot-Wire Ammeter:

1- It’s connected in series

2- When AC passes through the wire, temperature increases and wire will expand

3- The silk thread pulls the roller, so pointer will move on the scale

4- Pointer deflection is directly proportional with the current flow

5- When current stops the wire is cooled and roller will pull the pointer to zero

Disadvantages

- Pointer is slow in moving.

- It’s affected by the room temperature that may cause errors in readings

To overcome that we stretch the wire on a plate that has the same expanding coefficient of the wire material and

insulate it from wire

How to calibrate this device?

- Calibrating means to ensure that it’s working good and it can measure the correct effective value

- By comparing its reading with the reading of the moving coil Ammeter by connecting both in series in a dc circuit

with rheostat

Notices

- The scale is not regular because the thermal amount generated

in the wire is directly proportional with I2 , not I

- It can measure both AC and DC currents because the thermal

effect of current doesn’t rely on the current direction

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Laws

Capacitor

A. Capacitive reactance

XC= 1 / 2πfC = 1 / C B. Capacity

C = Q / V C. Compare between 2 capacitors capacitive

reactance

XC1/ XC2= f2 C2 / f1 C1 = C 2 / C1

D. AC current intensity in a capacitor

= VC / XC

E. Connecting Capacitors

a- In parallel

1/XC= 1/XC1+1/XC2 +1/XC3 +……

CT =C1+ C2 + C3

In case of capacitors are similar

CT = C1 *n

XC = XC1 / n

b- In series

XC= XC1+ XC2 + XC3 +……

1/CT = 1/C1 + 1/C2 + 1/C3

In case of capacitors are similar

CT = C1 /n

XC = XC1 * n

Laws

Inductive Coil

A. Inductive reactance

XL= 2 f L = L

B. Induction or (self-induction coefficient)

L = / L (length)

C. Compare between 2 coils inductive

reactance

XL1/ XL2= f1 L1 / f2 L2 = L 1 / L 2

D. AC current intensity in a coil

= VL / XL

E. Connecting inductive Coils

a- In parallel

1/XL = 1/XL1+1/XL2 +1/XL3 +……

1/LT = 1/L1+ 1/L2 + 1/L3

In case of coils are similar

L = L1 / n

XL = XL1 / n

b- In series

XL= XL1+ XL2 + XL3 +……

LT = L1+ L2 + L3

In case of coils are similar

LT = L1 * n

XL = XL1* n

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Laws

RL Circuit

V = √ VR2+ VL

2

Z = √ R2+XL2

Tan = VL/VR = XL/XR

is Positive

RC Circuit

V = √ VR2+ VC

2

Z = √ R2+XC2

Tan = - VC/VR

= -XC/XR

is Negative

Laws

RCL Circuit

V = √ VR2+ (VL- VC)2

Z = √ R2+(Xl-XC)2

Tan = (VL-VC) / VR

Tan =(XL-XC)/R

When XL> XC is Positive

When XL< XC is Negative

Resonance Circuit

A. Resonance circuit frequency

f = 1/2√ LC

B. To compare between two frequencies

f1 /f2 = √ (L2 C2 /L1 C1)

C. VL = VC

D. XL = XC

E. Z = R

F. I = V / R

G. 0

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Chapter 5

Definitions

1- Black Body

Is the body that can absorb all kinds of radiations of different wave lengths (ideal absorber) and re-emits them in

an ideal form (Ideal emitter

2- Planck’s Curve

It’s the curve that describes the relation between radiation intensity and wave length of spectrum emitted from

bodies

3- Wein’s Law:

The wavelength corresponding to maximum radiation intensity is inversely proportional with the temperature

on Kelvin scale

4- Remote sensing

It’s the technology of discovering the natural resources by imaging the earth surface using the different

spectrum regions (such as the infrared radiation)

5- Surface Potential Barrier

It’s the attraction force that used to attract electrons inside the metal and prevent it from exiting the surface

6- Thermionic emission (effect)

It’s the phenomena of emitting electrons from metal surface when heating

7- Photo-electric emission (effect)

It’s the phenomena of emitting electrons from the metal surface when a light beam of specific frequency falls on

the metal surface

8- Metal Work function

It’s the minimum energy required to free the electron from the metal surface

9- Critical (threshold) frequency

It’s the minimum frequency required to free the electron from the metal surface

10- Compton Effect:

When a high energy photon (Of X-ray or gamma-ray) collide with free electron, photon frequency will

decrease and its direction will change and electron velocity will increase and its direction will increase

11- Planck’s constant:

It’s the ratio between the photon energy and its frequency

12- Photon:

Is a quantum of energy uncharged and has a mass during its movement

13- De ’Broglie Equation:

The wave length for the wave corresponding a moving particle is equal to the ratio between the Planck’s

constant and linear momentum of the particle

What’s meant by?

1- Work function for iron equals 6.89*1014 J

The minimum energy required to free an electron from the iron metal surface is 6.89*1014 J

2- Critical wave length for a metal is 0.0002 m

It means that the highest wavelength required for the incident light to free an electron from the surface of this

metal is 0.0002 m

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What are conditions required to

1- Emitting an electron from metal surface

Answer:

A. Electron should gain a thermal or light energy bigger than or equal the metal work function

Or

B. The frequency of the incident light is bigger than or equal the critical frequency of the metal

2- Vision of a very small body using the electronic microscope:

Answer:

- The wave length corresponding the electron beam is smaller than the details of this body

Devices

Device Usage Scientific Idea

Remote sensing devices 1- Military applications Like night vision devices

2- Medicine: specially in Oncology and embryology

3- Discovering natural resources

Thermionic emission

Cathode Ray Tube CRT T.V. and Computers Monitors Thermionic emission Explain: emitting electrons from the metal surface when heating

Photo-Electric Cell Converting the light energy to electrical energy as in calculators and automatically (open/close) doors

Photo electric effect Explain: emitting electrons from the metal surface when a light beam with the critical frequency falls on this surface

Electronic Microscope Enlarging the very small objects Particle-Wave Duality Explain: it increase the speed of electrons by increasing the potential difference between cathode and Anode so ,electrons will gain large Kinetic Energy and large linear momentum which decrease the wave-length of the wave corresponding the electron beam until reaches the details of the small object which achieve the vision condition

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Usages:

Infra-Red Radiation 1- Discovering the natural resources 2- Night Vision Devices 3- Remote Sensing

Micrometer Waves Radars

Grid in the CRT Control the electron beam intensity

The electric and magnetic fields in CRT Control the direction of the electron beams to fall on the fluorescent screen dot by dot

Relations Diagrams

Relation between Diagram Used Law and Slope

Square of electron velocity v2 and Potential difference between Cathode and Anode V

eV = ½ mv2

Slope = Δv2/ΔV =2e/m

Photons Energy E and its

Frequency

E= h Slope=h

Kinetic Energy emitted from metal surface K.E. and frequency of incident light

hK.E.+ Ew

K.E.= hEw

Slope=ΔK.E/Δ

Energy E and Mass m

E= mC2

Slope= ΔE/Δm= C2

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Force (F)Affecting by an incident light beam on a surface and Power of the beam Pw

F= 2 Pw/C Slope= ΔF/ΔPw=2/c

Wave Length of wave corresponding a moving particle

and invert of the linear momentum (1/PL)

= h/ PL = h/mv Slope= h

Deductions:

1- Force resulted in falling a light beam of photons on a surface

Momentum of incident beam = mc

Momentum of reflected beam=-mc

Change of momentum = mc-(-mc) =2mc = 2h/c where m= hc2

Rate of falling photons on the surface= φL

Force is the time rate of change in momentum (Newton’s Law)

Then:

F= 2hφL /c

φL=1/Δt

F=2 h/ Δt.C

Power Pw= h/ Δt

Then

F = 2 Pw/C

2- Relation between the wave length of Photon and linear momentum of it

= c/

= hc / h= h / (h/c)

But PL= (h/c)

= h / PL = h / mc

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Factors that is depends on

Physical Quantity Factors that it depends on

Wave-Length corresponding the maximum Radiation intensity

Temperature in Kelvin

mT

/=T2/T1

Work Function of Metal

The material of this metal, Not on the intensity of light or time elapsed facing the light or the potential difference bet. Cathode and Anode

Generating electrical current from the photo-electric cell

The frequency of the incident light Not on the intensity of light or time elapsed facing the light

Intensity of the photo-electric Current The intensity of light Provided That > c

The Wave-Length Corresponding a moving particle

= h / PL = h / mv 1- Mass of the particle m 2- Velocity of the particle v

Comparisons

1- Sun radiation and Lamp radiation

Radiation of Sun Radiation of Lamp

- Kelvin Temperature of Sun Surface = 6000

- This makes the maximum radiation intensity falls in the region of Visible

light where m= 500 nm - 40% of sun radiation is visible light ,

50 % is infrared and the rest falls in the different spectrum regions

- Kelvin Temperature of glowing lamp = 3000

- This makes the maximum radiation intensity falls in the region of Infrared

where m= 1000 nm - 20% of lamp radiation is visible light

and the rest is infrared

2- Electron And Photon

Electron Photon

Nature Physical particle has a negative charge and has a wave nature

Quantum of energy uncharged, and has a wave and particle nature

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Speed increase capability We can increase its speed by the electrical field

We Cannot increase its speed Speed is constant in air = 3*10 m/s

Linear Momentum Pl=mv=h/ Pl=mc= h/= h/c

Mass It has a rest mass with a constant value me=9.1*10-31kg it still constant when it stops

It has a mass only when it

moves m= h/c2

When it stops its mass will vanished and converted to energy E= mc2

3- Microscopic model and macroscopic model of Light

Microscopic Model Macroscopic Model

1- It’s applied when the obstacle that collides the light photon is in size of atom or electron

2- The interatomic spaces of surface is larger than wavelength of incident light

3- It discusses the photon as a sphere with

radius r equal to the wave length of

light wave that has frequency 4- Light will penetrate the surface and deal

as a particle

1- It’s applied when the obstacle that collides the light photon is very large (to be larger than the wave length of the light wave)

2- The interatomic spaces of surface is smaller than wavelength of incident light

3- It discusses the photons as a package of has magnetic and electric fields that are perpendicular to each other and perpendicular to the direction of the wave direction

4- Light will reflects on the surface and deal as a wave

- Electronic Microscope and Optical Microscope

Electronic Microscope Optical Microscope

Used Beam Electrons of high energy Light from light source

Used Lens Electric or magnetic lens Optical-glass lens

Limits Of usage Magnifying very small bodies of dimensions smaller than wave length of light(like viruses)

Magnifying small bodies but its details are larger than the wave length of light

Final Image Received on a fluorescent screen or photographic plate

Received directly on eye

Magnifying Factor Very Big Limited

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Planck’s Interpretation for the black-Body radiation

1- Radiation is formed of units of energy called quantum which has energy E=hwhere h is Planck’s constant

and is the frequency

2- Photons are released as a result of stimulation of the atoms of the bodies

3- The stimulated atoms energy is insulated –not continuous- and takes levels of energy where the energy

value of each level is E= n hwhere n is the number of the level

4- Atoms don’t release radiations as long as they are stable in one energy level

5- When atom transfers from a higher level of energy to a lower level it releases a photon of energy E =

hand the emitted radiation is formed of billions numbers of photons and we noticed them as a wave i.e.

we cannot notice each photon as a single unit

6- The intensity of light is depending on the energy of a single photon and number of emitted photons

7- If frequency increased the energy of each photon increases and no. of photons decrease when the total

energy is constant

Cathode Ray tube Operation:

1- Cathode is heated up by a filament, so electrons are released from the electron gun by the thermionic effect

of heat (which get rid of the surface potential barrier)

2- Potential difference is generated between this cathode and the positively charged Anode so electron beams

will directed to the fluorescent screen which is connected to the Anode

3- When these electrons collide with the screen it makes light which is different in its intensity from point to

point on the screen according to the electron beam intensity

4- Grid controls the intensity of the electron beam, and the electromagnetic fields (vertical, horizontal) controls

the direction of this beam

Einstein Interpretation for the photo-electric effect

1- If photon energy is less than the surface potential function, no electrons will emitted from the surface regardless

the intensity of the light or the time elapsed facing the light

2- If the photon energy equals the surface potential function so electron will be hardly free from the surface but it

hasn’t kinetic energy to move, hence its frequency equals the critical frequency

3- If the photon energy is larger than the surface work function, the difference in energy will gained by electron as

a kinetic energy

Photo-electric Cell Operation:

1- It formed of a metal surface called Cathode

2- When light of critical frequency falls on Cathode, some electrons are released

3- Anode Picks up these electrons which cause a current flows in the external circuit

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Compton Phenomena:

- When a photon of (x-ray or Gamma-ray) collide with an electron

1- Photon frequency is decreased and it scatters and changes its direction

2- Electron speed is increased and it scatters and changes its direction

- Planck put hypothesis to this phenomena

1- This light radiation consists of photons, these photons can collide electrons as billiard balls

2- The sum of momentums for photons and electrons before collision equals the sum of them after

collision

3- The sum of energies for photon and electron before collision equals sum of them after collision

4- We should deal with photons as electrons as it has mass, velocity and linear momentum

Photon Properties:

1- Photon is a quantum of energy E=hwhere h is Planck’s constant and is the frequency

2- It has a mass m during its motion only, and a linear momentum and it move with the speed of light which is

constant regardless the value of frequency

3- When photon stops, all of its mass will be converted to energy gained by the body that stops the photon

4- It has a particle nature and a wave nature so it maintains the law of mass and energy conservation

What happens in these cases?

1- Heating-up a metal surface to a very high temperature

- Electrons will be emitted from the surface

2- Increasing the temperature of a glowing body? To the wave length corresponding the maximum intensity

- Wave-length corresponding the maximum intensity will be displaced to shortest value in the relation

mT

3- Photons falls on a surface of interatomic spaces is less than the wave length of photons

- Photons are reflected as they deals with this surface as a continuous surface and it acts with its wave nature

(reflection)

4- Photons falls on a surface of interatomic spaces is higher than the wave length of photons

- Photons will penetrate the surface and collide electrons around atoms, photons are act with its particle

nature

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Give reason

1- Light emitted from a glowing source is different according to difference in temperature

- As the glowing source doesn’t emits wave-lengths with the same values ,the wave length corresponding the

maximum intensity of radiation is inversely proportional with the kelvin temperature

2- The color of the radiation that result in heating the body changes from red to yellow to blue as the

temperature increased

- According to Wein’s Law the wavelength corresponding the maximum intensity is inversely proportional

with temperature so color is changed from red(which is the longest wavelength) then yellow (wavelength

less than red) then blue (very short wavelength)

3- We cannot see the radiations emitted from earth

- As earth has a small temperature then radiations have higher wavelengths which fall in the infrared region

which is invisible for the human

4- Classical physics doesn’t interpret the Planck’s curve

- As they consider Radiations as only electromagnetic waves so they think that the intensity of radiation

increases with increasing frequency , but Planck found that intensity of radiation leads to zero at very high

frequencies ( very low wavelengths)

5- Classical physics doesn’t interpret the photo-electric phenomena

- As they states that electrons will be emitted according to the intensity of light and the time elapsed facing

the light, but modern physics discovered that this emission if electrons depends on the frequency of light, it

should be higher than or equal the critical frequency

6- Electrons will be emitted from the surface of a specific metal when it receives a blue ray of light with a

lower intensity ,but it doesn’t emitted when it receives a very strong red ray

- As the blue ray has small wave length and high frequency which is higher than the critical frequency of this

metal regardless its intensity , and red is larger wavelength smaller frequency which is lower than the critical

7- Electrons may be released with a kinetic energy

- Because the energy of the incident photon is higher than the surface work function so the difference in

energy will be gained to electrons in form of kinetic energy

8- Anode in the photo electric cell is a thin wire

- To allow the incidence of light on Cathode

9- When a photon collide free electron the electron speeds up and photon frequency will decrease

- Because according to Compton phenomena the electron gained a part of photon energy so it converted to

kinetic energy ,photon will lose a part of its energy so frequency will decrease

10- Compton proved the particle nature of light

- As he proves that photon acts as electron and collide with it, and it has a mass and velocity and linear

momentum

11- When nucleus fission a huge quantity of energy is released

- Nucleus fission corresponds shortage in mass which is converted to energy E=mc2 the mass is low quantity

but the square value of light velocity= 9*1016 m2/s2

12- Light has a dual nature (particle and wave)

- Because the photons of light has a mass in motion and a velocity and linear momentum which are particle

properties and the light beam corresponds a wave has wave-length and frequency ,it can reflect, refract

,diffract and overlap

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13- Wavelength of the wave corresponding the electron beam is decreased when the linear momentum

increases

- According to De ‘Broglie equation

= h / PL = h / mv

Wave length is inversely proportional with the linear momentum

14- Force resulting on the light beam doesn’t affect a solid wall but it affects an electron

- Force F = 2 Pw/C and because the light speed is very high then force is very low which cannot affect solid

wall but it affects electrons as it has a very small mass and increases the electron speed

15- Optical Microscope cannot be used to view viruses

- As the condition of vision stated that : the wave length of the incident beam should be lower than the body

details

- Optical microscope uses light beam which has a wavelength bet 400-700 nm which is longer than the virus

details so it‘s unable to view it

16- When increasing potential difference between anode and cathode in electronic microscope the

wavelength of wave corresponding the electron beam decreases

- When increasing the p.d. the electron energy will increase and its speed will increase and its wavelength

decrease according to De ‘Broglie equation

= h / PL = h / mv

Laws

- Wein’s Lawm1/m2 = T2/T1

- Photo-Electric Effect

E = Ew + K.E.

E = hEw= h C = h C / C , K.E. = ½ m v2 = e. V

- Energy in joule = energy in electron.volt * Electron charge

- = C/ = E/h

- E = h = m C2= PL C

- PL= E / C = h C = h / = m C

- m = E / C2 = h C2 = h / C

- Pw= E φL = h φL

- F= 2 h/ Δt.C = 2 h φL / C = 2 Pw / C

e = 1.6 *10-19 C , h = 6.625*10-34 J.S , c =3*108 m/s , me= 9.1 * 10-31 kg

- De ‘Broglie equation

= h / PL = h / mv = h / mc

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Chapter 6

EE.Definitions

1- Spectrometer:

A device used to obtain pure spectrum by analyzing light to its visible and invisible components

14- Emission Spectrum

It’s the emission resulting from the transfer of an excited atom from a higher energy level to lower energy level

15- Continuous Spectrum

The spectrum consisting of all wavelengths in a continuous manner

16- Line spectrum

It’s the spectrum that occurs at specified frequencies and not continuously distributed

17- Absorption spectrum

Dark lines for some wavelengths in the continuous spectrum of white light, which resulting in the absorption of

the element vapor to the spectrum lines that is distinctive to it

18- Fraunhofer Lines

It’s Absorption spectrum for elements in the outer atmosphere of sun like atoms of Helium and Hydrogen

19- X-rays

It’s invisible Electromagnetic waves of high energy, high frequencies and very short wave-lengths and it falls

between wave-lengths of gamma-rays and ultraviolet rays

FF. What are conditions required to

3- Obtain pure spectrum from Spectrometer

Answer:

Prism should be placed in the minimum deviation position

paralleled rays for each color should be collected in focal plane using the objective lens

4- Obtain distinctive line spectrum for the objective material

Answer:

High potential difference should be applied between filament and objective in Coolidge tube to let

electrons gain high kinetic energy

One accelerated electron should collide with another electron which is existing near to one of nucleuses

of the objective material

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GG. Usages:

Spectrometer 4- Analyzing light to its visible and invisible components

5- Obtain pure spectrum 6- Estimating stars temperatures and its

gases

X-rays 1- Studying the Crystalline structure of materials

2- Detection of structural defects in the materials used in the metallurgical industry

3- Bone imaging and locating fractures or cracks

Filament in Coolidge tube 1- Electrons Source

High potential difference between filament(Cathode) and objective in Coolidge tube

1- Accelerating emitted electrons from Cathode Filament

HH. Comparisons 4- Hydrogen Spectrum Series

leyman’s Balmer’s Paschen’s Bracket’s Pfund’s

Cause of emission Electron transfer from higher levels to the first level K(n=1)

Electron transfer from higher levels to the second level L ( n = 2 )

Electron transfer from higher levels to the third level M ( n = 3 )

Electron transfer from higher levels to the forth level N ( n = 4 )

Electron transfer from higher levels to the fifth level O ( n = 5 )

Region of electromagnetic e.m. spectrum

Ultraviolet Visible light Infra-Red Infra-Red Very Far Infra-Red

Wavelength low wavelength high wavelength

frequency High Frequency low frequency

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Follow Comparisons 5- Continuous spectrum & Line spectrum (for X-rays)

Continuous spectrum for x-rays Line spectrum distinctive for x-rays

How energy is generated When accelerated electron that is emitted from Cathode passes near the electrons of atoms of the objective material its velocity and energy will decrease as a result of collisions and scattering

According to Maxwell theory, loss in electron energy will appear in a form of electromagnetic radiation that contains all available wavelengths because electrons lose their energy in a different amounts & different time length

When one of the accelerated electrons that are emitted from cathode collides another electron that are near to nucleus of one of atoms for the objective material, this other electron gains high energy makes it move to higher energy level or leave the atom and another electron from outside atom (which is in a higher energy level) will take its place

The difference in energy between the two levels will appear in a form of radiation of a specific wavelength can be specified from this relation:

ΔE = E2 – E1 = h c/

h c / ΔE

Factors on which wavelength depends on

The least value of wave length depends on potential difference bet. Filament and objective

mV

Wavelength doesn’t depend on objective material

It doesn’t depend on potential difference bet. Filament and objective

Wavelength depends on objective material ,wavelength decrease by increasing the atomic number

Naming Called brake –rays, soft radiation Called Intense radiation

Diagram

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II. Some Explanations Bhor’s Model for Hydrogen Atom (using Rutherford imaginations (

1- At the center of atom there is a positively charged nucleus

2- Negative electrons moves around nucleus in specific energy levels called shells, electrons don’t emit energy as

long as they move in its level of energy.

3- Atom is neutral as number of –ve charges (electrons) around nucleus equals number of +ve charges inside

nucleus

And he added three Hypotheses 1- Electrical forces (Coulomb’s Law) and mechanical forces (Newton’s Law) are applied inside atom

2- Radius of electron shell can be obtained by the relation 2 𝜋r = n

3- When electron transfers from higher energy level E2 to lower energy level E1 , a photon is released with energy

equals the difference between these two levels energy

ΔE = E2 – E1 = h

Bohr’s Interpretation for Linear Spectrum of Hydrogen atom

When stimulating Hydrogens atoms by gaining energy

1- They don’t stimulated with the same amount, so electrons transfer from first level K (n=1) to different

higher levels (2, 3, 4…)

2- Energy of any level En in Hydrogen atom can be calculated from relation

En= (13.6/n2) eV

Notice: Energy in joule = energy in eV * 1.6*10-19 (charge of electrons)

3- Electrons remain in higher levels for very short time about (10-8) and returns back to lower levels

4- When electrons return from higher levels to lower levels, it lose energy ΔE = E2 – E1 = h hc/

5- Linear Spectrum of Hydrogen atom is divided to 5 groups (5 chains)

Pfund’s

Bracket’s

Paschen’s

Balmer’s

Lyman’s

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JJ. Spectrometer

Device used to obtain pure spectrum by analyzing the white light to its visible and invisible components

Usages:

1- Obtain pure spectrum

2- Analyze white light to its visible and invisible components

3- Estimate temperature of stars and gases inside these stars

Structure:

1- White light source with a slit in a front of a convex lens

2- Turntable: with a prism place on it

3- Telescope of two lenses (objective and eye lens)

Work Operation:

1- When light beam falls on the slit the convex lens collects it to fall on the prism

2- Prism is placed in the minimum deviation position and it redirects the light beams to the telescope lenses

3- Prism will analyze white light so each color beams will be parallel to each other and not parallel to other colors

(As each color has a different deviation angle)

4- Objective lens will collect each color in a focal plane to be specified and viewed by the eye lens

KK. Coolidge tube

Structure

1- High potential difference source

2- Target of Tungsten

3- Filament used as source of electrons

4- Vacuum tube to place target and filament inside it

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How to obtain X-rays using Coolidge tube

1- When heating the filament, electrons will released towards the target under the effect of the electric field

2- These electrons will gain very high kinetic energy depending on the potential difference between Cathode

(filament) and Anode (target)

3- When electrons collide the target (Tungsten) its kinetic energy or part of it will converted to x-rays

X-rays Properties:

1- Very high ability to penetrate media

2- Very high ability to ionize gases

3- It diffracts when passing through crystals

4- It affects the accurate photographic plates

LL. What’s happened in these cases?

1- Exciting Hydrogen atoms by different amounts of energy

Answer:

- Electrons move to different higher energy levels (2,3,…) and they return back to the lower levels then it

emits energy equal to the difference between the two levels, this energy E =h is different in

wavelengths so it emits the 5 chains of spectrum for hydrogen atoms

2- Electron falls from higher energy level to lower energy level

Answer:

- it emits energy equal to the difference between the two levels E =h E2- E1

3- exciting an electron until it reaches higher level of energy

Answer:

- electron will remain for a very short time in the higher level and back again to lower level producing

energy equal to the difference between the two levels, E =h E2- E1

4- Electrons return back from higher energy levels to level M (n=3)

Answer:

- The emitted spectrum falls in the region of infrared radiation (Paschen’s)

5- Light white passing through gas or vapor and analyzing the resulting spectrum

Answer:

- Wavelengths or dark lines in continuous spectrum will appear, these wavelengths are itself the

wavelengths for the line spectrum which is distinctive to this gas

6- X-rays pass through crystals

Answer:

- Rays will diffract and then overlaps because it passes through the interatomic spaces of crystals atoms

composing dark hems and luminous hems ح شكل الكريستاالت(هدب مضيئة وهدب مظلمة )توض so it’s used in

studying crystalline structure

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7- X-rays pass through a gas

Answer:

- It ionizes the gas atoms as a result of high energy of x-rays

8- Electrons of high kinetic energy penetrate a target in Coolidge tube

Answer:

- Free electrons will collide another electron in the inner levels of target atoms so it’s scattered and

another electron of higher energy will replace the scattered electron generating high energy which is

X-rays

9- Replacing the target material with another material

Answer:

- Continuous spectrum will remain the same, but line spectrum will change as it depends on the material

of target

(Wave length of line spectrum will change if the material changed)

10- Replacing the target material with another one which is higher in atomic number

Answer:

- Continuous spectrum will remain the same, but line spectrum wave length will decrease and frequency

will increase so its energy will increase

11- Shedding تسليط low potential difference between filament and target in Coolidge tube

Answer:

- Continuous spectrum wavelength will increase and maybe the line spectrum will not appear

MM. Give reason 1- There are number of spectrum chains formed when exciting hydrogen atoms

- Because these atoms don’t be excited with the same degree, so atoms will move to different levels of

energy and return to different lower levels after a very small amount of time so it emits different

amounts of energy in different radiation regions

2- Lyman’s chain is the highest energy and pfund’s is the lowest

- In Lyman’s chain the electrons transfer from outer levels to the first level n =1 , so energy difference will

be maximum value, while in pfund’s the electrons transfer from outer levels to fifth level n = 5 so energy

difference will be minimum value

3- We can see Palmer’s series but cannot see Pfund’s

- Because Palmer’s spectrum wavelengths falls in the region of visible light but pfund’s falls in the region

of maximum Infra-Red radiation which is invisible

4- Line spectrum radiated only from material that is in state of separated atoms or in gas state under low

pressure

- Because the line spectrum results in transfer of excited atoms from high energy levels to lower energy

levels and materials cannot be excited except it was in this states (atomic states) not molecules state

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5- Appearance of dark lines when analyzing the sun spectrum, these lines called Fraunhofer lines

- As the sun spectrum is continuous and contains all available wavelengths but the outer atmosphere of

sun has some elements in gas state, these elements absorb its distinctive spectrum which appear in a

form of dark lines are the absorption spectrum of these elements

6- Using high voltage in Coolidge tube to generate X-rays

- To grant Cathode electrons high kinetic energy so after collision with target its energy converted to

radiation in form of X-rays

7- X-rays generated on Coolidge tube has a high frequency

- Because energy gained by electrons before collision with target is very high according to high potential

difference and it appears as a high frequency spectrum (with very low wavelengths)

8- Continuous spectrum appears in x-rays

- When accelerated electrons are closed to the target electrons, it loses its energy gradually on different

amounts as a result of collisions so the resulting spectrum contains continuous spectrum

9- Wave length of distinctive line spectrum of X-rays depends on the target material and not on the potential

difference between Cathode and Anode

- Because the distinctive line spectrum of X-rays results in collision of accelerated electrons with electrons

that are very near to the nucleus of target atoms which jumps to higher energy levels or leaves the atom

and another electron from other higher energy level will takes its place and the difference between the

two levels differs from material to another material so this difference appears in a form of line spectrum

of specific wavelength which is distinctive to the target material

10- X-rays has a very high ability to penetrate the atoms

- As it has a very high frequency and very low wavelength which is less than the interatomic distances of

atoms so it can penetrates

11- X-rays used in discovering the defects of materials used in Metallurgical Industries - As it has a very high ability to penetrate the interatomic spaces of these materials as its wavelength is

very small

-

12- X-rays used in diagnosis of fractures in bones - As x-rays penetrate bodies in different degrees so its penetration degree differs in case of fracture

bones and in case of healthy bones so it can specifies the places of fractures

13- X-rays used in studying the crystalline structure - As it has ability to differ when collide the crystals, so it then interfere and according to the interference

waves we can specify the structure of crystals

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NN. Laws

1- Specify energy of the shell (level)

En = (- 13.6 / n2) eV = (- 13.6 / n2) * 1.6 *10-19 Joule

2- Radius of shells (levels)

Rn = n./ 2 = n h / 2 m v

3- ΔE = E2 – E1 = h c/

Highest energy

E∞ - En = hc/ = h E∞ = 0)

Lowest Energy

E (n+1) – En = hc/ = h

4- X-rays emitted

E = h = hc/ 1/2 me v2 e V

5- Shortest wavelength of X-rays

=hc / E = hc / e V

6- Highest frequency of X-rays

= E / h = e V /h

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Chapter 7

OO. Definitions

2- Laser:

- Light Amplification by Stimulated Emission of Radiation

3- Lifetime

- The time elapsed by atom to lose its exciting energy and returns back to its original state

4- Spontaneous Emission

- It’s automatic release of radiation from excited atom when it moves from higher energy level to lower

energy level after lifetime end

5- Stimulated emission

- It occurs when an external photon stimulates excited atoms to emit new photon of energy equals the

difference between the excited level and the low level

6- inverse-square law

- the incident light intensity on a surface is inversely proportional with the square distance between that

surface and the light source

7- Optical Pumping process:

- It’s the process of exciting the active medium atoms to generate laser by light energy

8- Population Inversion State:

- It’s the state in which number of active material atoms in the higher energy levels bigger than its number in

lower energy levels

9- Meta-stable excitation level:

It is an energy level characterized by a relatively long lifetime 10-3 s

10- Hologram

- It’s a 3-D image which is formed as a result of interference of the Reference beams with the reflected beams

on the body

11- Reference Beams:

- Parallel beams used in 3-D imaging these beams has the same wave-length for the reflected beams on the

body

PP. Scientific Ideas

Laser Theory Idea: stimulated emission

Explanation: - Atoms or molecules of medium reach

population inversion state - Photons released from excited atoms by

the stimulated emission - Amplifying the released beam by

stimulated emission inside the resonant cavity

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3-D Photography (Holography) Idea: Laser Explanation:

1- In 3-D Photography other beams with the same wavelength of reflected beams on body which called reference beams meet with reflecting beams having all information of the body at a photographic plate

2- When photographic plate is

developed there are interference fringes appear which is called Hologram

3- When lighting this hologram using

Laser beam which has the same wavelength for the reference beams we can see a 3-D image for the body

QQ. Usages:

Radio frequencies source in Laser Granting atoms or molecules of active medium the required energy for excitation

The highly frequency electric field in (Ne-He) (Neon-Helium) Laser

It excites Helium atoms to higher energy levels

Helium atoms in in (Ne-He) (Neon-Helium) Laser

It transfers the excitation energy to Neon atoms and this helps reaching the population inversion state

Neon atoms in Ne-He) (Neon-Helium) Laser

It’s the active medium in (Neon-Helium) Laser as it reaches the population inversion state this causes the stimulated emission to generate laser

The reflecting mirror in Laser Generating Tube

It reflects photons which move in the direction of the tube axis, during this process, some photons collide with Neon atoms existing in Meta-stable excitation level and its lifetime doesn’t end so these Neon atoms emits coherent photons which are doubled so this is how light is amplified

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Reference beams Used in the holography as it meets the beams reflected on a body at the photographic plate which bears all the body information and appear as interference fringes

RR. Comparisons

6- Spontaneous and Stimulated emission

Spontaneous Emission Stimulated Emission

How does it happen?

When excited atom transfers from higher exciting level to lower exciting level after the end of lifetime and without any external effect

When excited atoms transfers from higher exciting level to lower exciting level by the effect of incident photon has the same energy of photon causing the excitation of atoms before the end of lifetime

Diagram

Emitted Photons Properties

1- Emitted photons has the same frequency of the original photon but not the same phase or direction

2- Emitted photons fall in large range of frequencies in the electromagnetic spectrum

3- Photons propagate randomly in all directions

4- Radiation intensity decreases during propagation as it follows the inverse-square law

1- Two coherent photons are equal in frequency and move in same phase and direction

2- Emitted photons has only one wavelength

3- Photons propagate in one direction in form of coherent and paralleled beams

4- Intensity is constant during propagation even for a long distance as it doesn’t follow the inverse-square law

Examples - Ordinary light sources - Laser sources

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7- Ordinary light and laser

Ordinary light Laser

Spectral Purity 1- Emitted photons has large range of wavelengths (it has wide spectrum range) so when we see light white by eyes we can see its different colors in spectrum 2- lamination intensities are different in wavelength

1- Emitted electrons has a very small range of wavelengths (it has narrow spectrum range)

2- the intensity is concentrated in a specific wavelength so it’s considered a monochromatic light with a single wavelength

Light beam collimation

The light package diameter increased during its propagation as a result of scattering

Laser beams continue parallel for long distances and don’t scatter

Coherence Ordinary light photons are not coherent as : Laser photons are coherent as:

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- They are released from source in different time

- The propagates in variable difference in phase

- They are released from source in the same moment

- They propagate in constant difference in phase

Intensity Subject to يخضع ل the inverse square law, so intensity of incident light on a surface decreases by increasing the distance between source and surface

Doesn’t subject to the inverse square law, so intensity of incident laser beam remains constant in short or long distance as laser photons are very coherent and propagate without scattering

8-

Ordinary photography Holography (3-D photography

Type of image 2-D image (flat) 3-D Image

Information recorded on image Photographic plate records parts of information that are taken from the reflected beams, this parts is the difference in light intensity only

Photographic plate records all information that are taken from the reflected beams and they

- differs in light intensity - differs in beams path

length = path

difference * 2/ path length which results in the difference of topology of body or difference in phase of light waves

-

SS. Some Explanations

Basic elements of Laser 4- Active medium: it’s the active material for producing Laser beam, it may be

A. Sold crystals: as ruby Laser

B. Semi-conductor solid material: as Silicon crystals

C. Liquid dyes: as organic dyes dissolved in water

D. Gaseous atoms: as the (Helium-Neon) gas Mixture

E. Ionized gases: as ionized Argon

F. Gaseous Molecules: as carbon dioxide gas

5- Energy sources: responsible for exciting the active medium atoms as

A. Electric energy: by (electric discharge using high direct potential difference, or using radio frequency

sources)

B. Light energy: called light pumping by ( using glowing lamps as in Sapphire Laser, or using Laser beam as in

Liquid dyes)

C. Thermal energy: using the thermal effect resulted in the pressuring gases for exciting materials that can

emit Laser

D. Chemical energy: chemical reactions produce energy that is used in producing stimulated radiation (Laser)

as used in reaction of Hydrogen and Floor or reaction of deuterium florid and carbon dioxide

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6- Resonance Cavity: which is the container that contains the active material and it’s responsible for the

amplification process, and it’s two types:

A. External resonance cavity: formed of two reflecting mirrors to hold the active material between them, this

cavity is used in Gases Laser(He, Ne) Laser

B. Internal resonance cavity: the two ends of the active material are paint to work as two reflected mirrors,

one of them is semi-transparent to allow passage of generated Laser beams, this cavity used in the Laser of

solid material like Ruby Laser

He – Ne Laser 1- Device structure

A. Quartz tube has a mixture of Helium and Neon gases in ratio of (10:1) under low pressure of

0.6 mmHg

B. Two paralleled mirrors and normal to the tube axis on of them is reflecting (reflection

coefficient 99.5%) and the other is semi-transparent (reflection coefficient 98%)

C. High DC Voltage discharged in the gases mixture to excite the atoms

2- Operation

A. High voltage will excite the Helium atoms

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B. Helium Atoms will collide with the stable Neon atoms inelastic collision and according to the

near equality of their exciting levels, the exciting energy transfer from He to Ne

C. Continuous collisions between them results accumulation of neon atoms in an exciting level of

Relatively high lifetime about 10-3 s called metastable exciting level thus the condition of the

population inversion is achieved (this is the condition of Laser to take place)

D. Some neon atoms returns to lower levels of energy, then they release photons of energy equal

the difference between the two levels, these photons propagate randomly in all directions inside

the tube

E. Photos that move in the direction of the tube axis or paralleled to it collide with one of the two

mirrors and reflect internally and make several reflections between the two mirrors inside the

cavity

F. During the movement of these photons, they reflect with some Neon atoms that doesn’t finish

their lifetime in the metastable level, So Stimulated Emission takes place and each atom will

generate two photons of the same frequency, phase and direction

G. These steps repeat several times and in each time the number of stimulated photons is doubled

until we obtain an Amplified beam

H. When this radiation reaches a certain level, part of it exits the semi-transparent mirror in form

of Laser and the rest of radiation remains inside the tube to continue the process of stimulated

emission

I. Neon atoms that returned to lower level lose their energy in form of thermal energy and they

returns to the earth level and the process repeats ( they collide with Helium atoms)

J. Helium atoms that lose their energy by collision with the Neon atoms will be excited again by

the discharging DC Voltage inside the tube and so on …..

Laser Applications

1- Holography

2- Medicine: laser beams used is diagnosis, operative surgeries, far and near sightedness, and retinal detachment

3- Communication: Laser with optical fibers used in data networks

4- Manufacturing field : vaporizing the iron

5- Military field: smart bombs, Laser Radar (LADAR), missile guidance

6- Computers: CDs and Laser Printers

7- Arts and Shows

8- Surveying

9- Space Research

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G. What happens if? A. Ending the lifetime of optical excited atoms

Or the transfer of atoms from higher levels of to lower levels after the lifetime end

- Atoms return back to earth level and photon is released of the same energy of the photon causing the

excitation

B. The transfer of atoms from higher levels of to lower levels before the lifetime end

- Stimulated emission takes place and atoms transfer from higher levels to lower levels and two coherent

photons are equal in phase, energy are released (their energy equals the difference of the two levels

energy)

C. Photon of energy (E2-E1) passes through an excited atom of level E2

- Atom returns back to level E1 and two coherent photons are equal in phase, energy are released (their

energy equals the difference of the two levels energy) by stimulated emission

D. Helium atoms exist lonely in the Laser tube

- No Laser is emitted

E. Atoms of active medium reach the population inversion state

- Stimulated emission happens

F. No reflecting mirrors in the ends of the active medium

- No reflections happen for photons and no amplification will happen ,no Laser will emit

G. Hologram excited with Laser beams have the same wavelength of the reference beams

- A 3-D identical image is appeared on photographic plates

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H. Give Reasons 1- Stimulated emission is happened

- when photo of energy h = E2-E1 collide with an excited atom which exists in level E2 and before the end of

lifetime, photon will stimulate the atom to emit its excitation energy in form of another photon has the

same energy, phase ,direction of the incident photon so two coherent photons are released and atom

returns to the earth level

2- although there are two photons are emitted by the effect of one photon , this is not a violation of the

energy conservation law

- because one of them is the incident photon and the other results in the transfer of atom from higher level to

lower level

3- Spectral purity of the Laser beam

- As Laser beams has the same wavelength

4- Laser beams can transfer long distances without any energy loss

- As Laser beams are released in a paralleled package and they are coherent so they doesn’t scatter

5- Laser is not subject to the inverse square law

- As Laser beams are paralleled and coherent so its intensity doesn’t change inversely with the square

distance between the source and the body

6- Existence of two reflecting mirrors, one of them is semi-transparent at the ends of the (He-Ne) Laser

tube

- To make series of repeated reflections for photons resulting from the stimulated emission process so these

photons collide with some Neon atoms which are exist in the metastable excitation level, photons will

stimulate these Neon atoms to release new photons , so number of photons are doubled with each

reflection and radiation is amplified until a certain level then it’s emitted through the semi-transparent

mirror

7- In Laser sources the active medium should derived to the population inversion state, but in ordinary

light sources this condition is not required

- As the scientific idea of Laser depends on existence of large number of atoms in the meta-stable level to

achieve the stimulated emission

8- The mixture of Helium and Neon gases is suitable to generate Laser

- Due to the near equality of their meta-stable excitation levels

9- We can obtain 3-D image only by using Laser

- To obtain 3-D image we should use coherent photons to indicate the difference in (illumination intensity and

phase) for the interference fringes of these photons and this is achieved only in Laser

10- Laser is used in the retina detachment cases

- The thermal effect of the paralleled Laser beams can be used in the retina cells fusion

11- Laser used as a missile guidance in military fields

- As Laser beams are paralleled and its intensity doesn’t changed by increasing distance so it’s suitable to

guide the rockets for very long distances