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Lecture 2 Basic Circuit Laws

Analogue electronics lec (2)

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Page 1: Analogue electronics lec (2)

Lecture 2

Basic Circuit Laws

Page 2: Analogue electronics lec (2)

2

Basic Circuit Laws

2.1 Ohm’s Law.

2.2 Nodes, Branches, and Loops.

2.3 Kirchhoff’s Laws.

2.4 Series Resistors and Voltage Division.

2.5 Parallel Resistors and Current Division.

2.6 Wye-Delta Transformations.

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2.1 Ohms Law (1)

• Ohm’s law states that the voltage across a resistor V(v) is directly proportional to the current I(A) flowing through the resistor.

• When R=0 short circuit

• When R= open circuit.

IR

IRV

R

R

IV

VVV

ab

ab

baab

Resistance

alityproportion ofconstant

a

b

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2.1 Ohms Law (2)• Conductance is the ability of an element to

conduct electric current; it is the reciprocal of resistance R and is measured in siemens.

• The power dissipated by a resistor:

v

i

RG

1

R

vRivip

22

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2.4 Series Resistors and Voltage Division (1)

• Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.

• The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.

• The voltage divider can be expressed as

N

n

nNeq RRRRR1

21

vRRR

Rv

N

n

n

21

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321)(

321)(

VVVV

IIII

Totalseries

Totalseries

As the current goes through the circuit, the charges must USE ENERGY to get

through the resistor. So each individual resistor will get its own individual potential

voltage). We call this voltage drop.

is

series

seriesTT

Totalseries

RR

RRRR

RIRIRIRI

IRVVVVV

321

332211

321)(

)(

;Note: They may use the

terms “effective” or

“equivalent” to mean

TOTAL!

2.4 Series Resistors and Voltage Division

(1)

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ExampleA series circuit is shown to the left.

a) What is the total resistance?

b) What is the total current?

c) What is the current across EACH resistor?

d) What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately)

R(series) = 1 + 2 + 3 = 6W

V=IR 12=I(6) I = 2A

They EACH get 2 amps!

V1W(2)(1) 2 V V3W=(2)(3)= 6V V2W=(2)(2)= 4V

Notice that the individual VOLTAGE DROPS add up to the TOTAL!!

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2.5 Parallel Resistors and Current Division (1)

• Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

• The equivalent resistance of a circuit with N resistors in parallel is:

• The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:

Neq RRRR

1111

21

n

eq

n

nR

iR

R

vi

Page 9: Analogue electronics lec (2)

2.5 Parallel Resistors and Current Division (1)

• Parallel wiring means that the devices are connected in such a way

that the same voltage is applied across each device.

• Multiple paths are present.

• When two resistors are connected in parallel, each receives current

from the battery as if the other was not present.

• Therefore the two resistors connected in parallel draw more current

than does either resistor alone.

321

321

321

321

1111

)(

;

RRRR

R

V

R

V

R

V

R

V

R

VIIIII

IRVVVVV

p

parallel

parallelT

Total

R3

i iP RR

11

I3

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Example 4

454.0

1454.0

1

9

1

7

1

5

11

P

p

P

RR

R

)(8 RI

IRV

To the left is an example of a parallel circuit.

a) What is the total resistance?

b) What is the total current?

c) What is the voltage across EACH resistor?

d) What is the current drop across each resistor?

(Apply Ohm's law to each resistor separately)

2.20 W

3.64 A

8 V each!

WWW9

8

7

8

5

8975 III

IRV

1.6 A 1.14 A 0.90 A

Notice that the

individual currents

ADD to the total.

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Gustav Kirchhoff

1824-1887

German Physicist

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2.2 Nodes, Branches and Loops (1)

A branch represents a single element such as a

voltage source or a resistor.

A node is the point of connection between two

or more branches.

A loop is any closed path in a circuit.

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2.2 Nodes, Branches and Loops (2)

Example 1

How many branches, nodes and loops are there?

4 Branches

3 Nodes

4 loops

Original circuitEquivalent circuit

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2.2 Nodes, Branches and Loops (3)

Example 2 Should we consider it as one

branch or two branches?

How many branches, nodes and loops are there?

7 Branches

4 Nodes

4 loops

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2.3 Kirchhoff’s Laws (1)

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

01

N

n

niMathematically,

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Junction Rule

Conservation of mass

Electrons entering must

equal the electrons leaving

The junction rule states

that the total current

directed into a junction

must equal the total current

directed out of the junction.

Page 17: Analogue electronics lec (2)

Kirchhoff’s Current Law

At any instant the algebraic sum of the

currents flowing into any junction in a circuit is

zero

For exampleI1 – I2 – I3 = 0

I2 = I1 – I3

= 10 – 3

= 7 A

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2.3 Kirchhoff’s Laws (3)

Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is

zero.

Mathematically, 01

M

m

nv

Page 19: Analogue electronics lec (2)

Kirchhoff’s Voltage Law

At any instant the algebraic sum of the

voltages around any loop in a circuit is zero

For example

E – V1 – V2 = 0

V1 = E – V2

= 12 – 7

= 5 V

Page 20: Analogue electronics lec (2)

Example 14 Using Kirchhoff’s Loop Rule

Determine the current in the circuit.

( ) ( ) 21

drops potentialrises potential

0.8V 0.6 12V 24 WW II

A 90.0

I 20 V 18

I

i

iV 0

( )321 VVVVbattery

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2.3 Kirchhoff’s Laws (4)Example 5

Applying the KVL equation for the circuit of the figure below.

Va-V1-Vb-V2-V3 = 0

V1 = IR1 V2 = IR2 V3 = IR3

Va-Vb = I(R1 + R2 + R3)

321 RRR

VVI ba

Page 22: Analogue electronics lec (2)

Loop Rule

The loop rule expresses conservation of

energy in terms of the electric potential.

States that for a closed circuit loop, the total

of all potential rises is the same as the total of

all potential drops.