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CHAPTER 3 : RESISTOR

Definition of resistor

- The resistor is defined as a component or material that may prevent or limit the current flowin the circuit. It also produces a voltage drop and dissipate energy.

- The symbol for resistance is R.- Unit is ohm (Ω).

- Symbol of resistance

- Types of ResistorsIn general the resistor can be divided into two groups!

i) fi"ed resistorsii) variable resistor

i) Fixed Resistors

#i"ed resistor - the value of a resistor can be obtained from the color code

Tolerance is the relief of actual value. The smaller of tolerance value the moreaccurate reading of the resistor.

Rated power is the ma"imum power that can be accepted by the resistance withoutincurring damage. If the power is e"ceeded the resistor will be damaged by e"cessiveheat.

Stabilit is the ability of a resistor to maintain the resistance value even the ambienttemperature are change.

ii) !ariable resistor

$ariable resistor is a resistor that can be changed by moving the contact resistance

elements. $ariable resistor is used in circuits that re%uire changes in current and voltage.

There are two ma&or types !

a) Rotary: The most common for of variable resistor or potentiometer is a rotary version.

This versions of potentiometer uses a rotary motion to move the slider around a trac' that

compromises most of a circle with contacts at either end of the trac' in the area where

part of the circle is missing. This form is widely used with 'nobs on a spindle for the actual

1

#i"ed resistor $ariable resistor

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control and they are found in many applications from providing ad&ustments on test

e%uipment through to being used for volume controls on domestic radios.

b) Slider: Slider controls are those variable resistors that slide in a linear fashion i.e. in a

straight line. These controls ta'e up more front panel space but are much easier to use

under some circumstances. #or e"ample they are widely used for audio mi"ers and

lighting des's. The advantage of sliders is that it is easier to control them %uite precisely

and compare the relative positions of a number of sliders. It is also possible to control a

number of sliders together.

" Factor affectin# resistance

The value of resistance is influenced by several factors as follows

a) The length of the conductor (wire) ()

Unit of length is meter (m).The resistance is proportional to the length of conductor.

b) *ross-sectional area of conductor (+)

Unit of *ross-sectional area is in s%uare meters (m,).The resistance is inversely proportional to the cross-sectional area (+) of conductor R .

hich is the smaller cross-sectional area (+) of conductor may effect the higher resistancevalue.

c) Type of substancesmaterial

ρ or resistivity is representing the nature or type of conducting material.

d) Temperature (T)

FOR$%&A

2

R α A L

ρ α R

R α ρ

+

R α

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E'ERCISE :

/. 0iven a resistance copper wire is ,/1 . The length of wire is ,22m and the thic' of wire is

2.3mm. *alculate a resistance (p) for this wire .

,. The resistance of conductor wire is ,2 1. The cross-sectional area of the conductor is 2.234m,

and a resistance is 2.35/ 1 m. *alculate how long the conductor.

Resistor color code

Resistor color code used in a small resistor. Resistor value is found by reading the lines on the

resistor color code. The table below shows the resistor color code table. 6ost resistors have four

bands. The first three lines give the reading of a nominal value of the resistor while the fourth band

indicates the tolerance.

Resistor commonly has four bands. Table / shows the value of colour band for a resistor.

Colo(rs )and *Di#it *

)and +Di#it +

)and 3$(ltiplier

)and ,Tolerance

7+*8 2 2 / -

7R9: / / /2 -

R;< , , /22 -9R+:0; 4 4 /222 -

=;9 3 3 /2222 -

0R;;: > > /22222 -

7U; ? ? /222222 -

$I9;T @ @ /2222222 -

0R;= A A /22222222 -

BIT; 5 5 /222222222 -

09< 2./ ± >C

SI$;R 2.2/ ± /2C

:9:; ± ,2C

Table /

3

RESISTOR CO&OR CODE

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Exa-ple

Satu perintang mempunyai &aluran warna beri'ut ! 'uning ungu merah dan emas.

Tentu'an !

i) :ilai namaan

ii) Dulat nilai sebenar rintangan

Eenyelesaian!

i)

8uning Ungu × 6erah Bad terima

3 @ × /22 F 3@22Ω atau 3.@ 'Ω

ii) Dalur had terima ialah emas iaitu ± >C.

had terima F ± 3@22Ω × 2.2>

F ± ,4>Ω

9leh itu &ulat nilai rintangan F (3@22Ω G ,4>Ω) F 354>Ω (had atas)

hingga F(3@22Ω - ,4>Ω) F 33?>Ω (had bawah)

Series. parallel and series /parallel connections

There are two basic ways in which to connect more than two circuit components! series and parallel .

a0 SERIES CO11ECTIO1

4

http://en.wikipedia.org/wiki/File:Resistors_in_series.svg

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The basic idea of a HseriesH connection is that components are connected end-to-end in a lineto form a single path for electrons to flow!

T2e properties of series circ(its

a. Resistance total

Rt R* 4R+ 4R3

Exa-ple:

ets start with a series circuit consisting of three resistors and a single battery!

the total resistance of any series circuit is e%ual to the sum of the individual resistances

5

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b) PARALLEL CIRCUITS

The basic idea of a HparallelH connection is that all components are connected across each othersleads.

:ow lets loo' at the other type of circuit a parallel configuration!

If two or more components are connected in parallel they have the same potential difference (voltage)across their ends.

The total current I is the sum of the currents through the individual components in accordance with8irchhoffJs current law.

The current in each individual resistor is found by 9hms law. #actoring out the voltage gives

.

To find the total resistance of all components add the reciprocals of the resistances R i of each

component and ta'e the reciprocal of the sum.

.

6

http://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws#Kirchhoff.27s_current_law_.28KCL.29http://en.wikipedia.org/wiki/Ohm's_lawhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Multiplicative_inversehttp://en.wikipedia.org/wiki/File:Resistors_in_parallel.svghttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws#Kirchhoff.27s_current_law_.28KCL.29http://en.wikipedia.org/wiki/Ohm's_lawhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Multiplicative_inverse

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#or only two resistors the unreciprocated e"pression is reasonably simple!

This sometimes goes by the mnemonic Hproduct over sumH.

#or N e%ual resistors in parallel the reciprocal sum e"pression simplifies to!

.

and therefore to!

.

c0 CO$P&E' CIRC%IT

Terdapat d(a 5aeda2 penelesaian ba#i litar 5o-ple5:

i0 6aeda2 sat( persat(

;"ample /

#ind the resistor total is shown the circuit below

Solution

Ω==+

×== 667.0

3

2

12

121//2

a R Ω==

+

×== 2.1

5

6

23

232//3

b R

7

/

,+

/ > 2

,

7

4

, 2 2

Ra Rb

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Ω=

+++=

+++=

667.351

2.1200667.0150

200150

T

T

baT

R

R

R R R

;"ample ,

+ more comple" e"ample of a series-parallel resistor circuit is shown below

Solution

Using the same procedure as above we first wor' out the e%uivalent resistance of each of the

parallel combinations to get the effective resistance in series with R 1. e begin with the

resistors R 4 and R 5

R 5-4 *78*739 4 *7,0 +;

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So all that is left is to wor' out the effective resistance of the parallel combination R 6-5-4 and

R 3-2

R 6-5-4-3-2 *78*7*;; 4 *7>

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Pi"connected and E@(ialent Delta 1etwor5<

For-(la fro- Delta to Star Conersion

3 R 1 R

2 R

#igure 4./? (a) shows three resistors and connected by a delta between the terminals + 7 and *.

The three resistors can be replaced by resistors Ra Rb and Rc are &oined by a star (#igure 4./? (b).

R AB F 1 R // ( 2 R G 3 R ) F)(

)(

321

321

R R R

R R x R

++

+ F

321

3121

R R R

R R R R

++

+ NN.. (i)

R BC F 2 R // ( 1 R G 3 R ) F)(

)(

312

312

R R R

R R x R

++

+ F

321

3221

R R R

R R R R

++

+ NN (ii)

and

10

R a

RbRc

A

BC

A

BC

Fi#(re 3

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R AC F 3 R // ( 1 R G 2 R ) F)(

)(

213

213

R R R

R R x R

++

+ F

321

3231

R R R

R R R R

++

+ NN (iii)

#igure 4./? (b) the resistance between terminals + and 7 are

R AB F Ra G Rb NNNNNN.. (iv)

R BC F Rb G Rc NNNNN...(v)

R AC F Ra G Rc NNNNNN(vi)

*onnect the e%uations from #igure 4./? (a) and (b) then

Ra G Rb F321

3121

R R R

R R R R

++

+ NNNNN(/)

Rb G Rc F 321

3221

R R R

R R R R

++

+

NNNNN.(,)

Ra G Rc F321

3231

R R R

R R R R

++

+ NNNNN.(4)

;%uation (/) - (,)

Ra - Rc F321

3231

R R R

R R R R

++

−NNNNN.(3)

;%uation (4) G (3)

,Ra F321

312

R R R

R R

++

Ra 321

31

R R R

R R

++ NNNN..(/./)

Rb 321

21

R R R

R R

++ NNNN..(/.,)

and Rc 321

32

R R R

R R

++NNNN..(/.4)

*onversion formula from Star to

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R 3 F Rb

Rc R1

Tu'arganti'an R 2 dan R 3 'e dalam persamaan (/)

Ra G Rb F)/()/(

)/()/(

111

1111

Rb Rc R Ra Rc R R

Rb Rc R R Ra Rc R R

++

+

F)]/()/(1[

)]/()/[(

1

111

Rb Rc Ra Rc R

Rb Rc R Ra Rc R R

++

+

F RaRc RbRc RaRb

RaRc R RbRc R

++

+ )]()[( 11

F RaRc RbRc RaRb

RaRc RbRc R

++

+ )(1

R1 F )(

))((

Rb Ra Rc

RaRc RbRc RaRb Rb Ra

+

+++

R1 Ra 4 Rb 4 Ra Rb

Rc

R 2 Rb 4 Rc 4 Ra

RbRc

R 3 Ra 4 Rc 4 Rb

RaRc

R 3 R1

R 2

12

A

BC

Ra

RbRc

Fi#(re 3

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Ra F321

31

R R R

R R

++

R1 F Ra G Rb G Ra Rb

Rc

Rb F321

21

R R R

R R

++ R 2 F Rb G Rc G

Ra

RbRc

Rc F321

32

R R R

R R

++ R 3 F Ra G Rc G

Rb

RaRc

Exa-ple

#ind the value of resistance for this circuit

>Ω ?Ω

Solution

Ra F685

85

++

× F ,./2>Ω Rc F

685

68

++

× F ,.>,?Ω

Rb F685

65

++

× F /.>@5Ω

13

Y Y

8Ω

Ra Rc

Rb

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BAB 3: pearuh