1

CHAPTER CHAPTER 22

EET 101 [Electric Circuit I]: EET 101 [Electric Circuit I]: V2009V2009

School of Computer and School of Computer and Communication Engineering, Communication Engineering,

UniMAPUniMAP Prepared By: Prepared By:

Wan Nur Suryani Firuz bt Wan Ariffin Wan Nur Suryani Firuz bt Wan Ariffin Amir Razif A. b. Jamil AbdullahAmir Razif A. b. Jamil Abdullah

Resistive Resistive CircuitCircuit

2

RESISTIVE RESISTIVE CIRCUITCIRCUIT

Series/parallel resistorSeries/parallel resistor Voltage divider circuitVoltage divider circuit Current divider circuitCurrent divider circuit Voltage and current Voltage and current

measurementmeasurement Wheatstone bridgeWheatstone bridge Delta-wye (Pi-Tee) Delta-wye (Pi-Tee)

equivalent circuitequivalent circuit

3

SERIES/PARALLEL SERIES/PARALLEL RESISTORRESISTOR

Resistors in series:

1R

SV

2R NRI

1V NV 2V

eqRSV

I

Resistance equivalent

Req = R1 + R2 + ……….+ RN

4

Current in Series Current in Series CircuitCircuit

Current in series circuit is same at all circuit elements

NIIII 21

VOLTAGE IN SERIES CIRCUIT

Voltage (VT) in series circuit is the total of voltage for each elements.

NT VVVV ..21

5

Resistors in Resistors in ParallelParallel

1RSI2R NR

1I

V

eqR

2INI

V

SI

6

Equivalent Resistors in Parallel:Equivalent Resistors in Parallel:

Neq RRRR

1............

111

21

N

eq

RRR

R1........11

1

21

7

Two resistors in parallel:

21 RRReq

21

21

21

111

RR

RR

RR

Req

8

Current in Parallel Current in Parallel CircuitCircuit

Currents in parallel circuit is the total of current for each elements.

NIIII ..21

VOLTAGE IN PARALLEL CIRCUIT

Voltage (VT) in parallel circuit is same at all circuit elements.

NT VVVV 21

9

Example Example #1 #1

Find the equivalent resistor (Req) in the circuit.

10

RESISTIVE CIRCUITRESISTIVE CIRCUIT

Series/parallel resistorSeries/parallel resistor Voltage divider circuitVoltage divider circuit Current divider circuitCurrent divider circuit Voltage and current Voltage and current

measurementmeasurement Wheatstone bridgeWheatstone bridge Delta-wye (Pi-Tee) Delta-wye (Pi-Tee)

equivalent circuitequivalent circuit

11

Voltage DividerVoltage Divider

222

12

Using Ohm law, we will get:

Voltage at resistor R2:

IRV 22 21 RR

VI

21

2

2122 RR

RV

RR

VRV

13

RESISTIVE RESISTIVE CIRCUITCIRCUIT

•Series/parallel resistorSeries/parallel resistor•Voltage divider circuitVoltage divider circuit•Current divider circuitCurrent divider circuit•Voltage and current Voltage and current

measurementmeasurement•Wheatstone bridgeWheatstone bridge•Delta-wye (Pi-Tee) equivalent Delta-wye (Pi-Tee) equivalent

circuitcircuit

14

Current DividerCurrent Divider

1R 2R

1I

V2I

_

I

15

From the Ohm’s law, (1)

21

212211 RR

RRIRIRIV

IRR

RI

IRR

RI

21

12

21

21

16

Series/parallel resistor Voltage divider circuit Current divider circuit Voltage and current measurement

Wheatstone bridge Delta-wye (Pi-Tee) equivalent circuit

RESISTIVE RESISTIVE CIRCUITCIRCUIT

17

Voltage and Current Measurement

An ammeter is an instrument designed to measure current.

It is placed in series with the circuit element whose current is being measured.

An ideal ammeter has an equivalent resistance of 0Ω and functions as a short circuit in series with the element whose current is being measured.

18

A voltmeter is an instrument designed to measure voltage.

It is placed in parallel with the element whose voltage is being measured.

An ideal voltmeter has an infinite equivalent resistance and thus functions as an open circuit in parallel with the element whose voltage is being measured.

19

A

V2R

1R

sV

The configurations for an ammeter and voltmeter to measure current and voltage

20

RESISTIVE RESISTIVE CIRCUITCIRCUIT

Series/parallel resistor Voltage divider circuit Current divider circuit Voltage and current measurement

Wheatstone bridge Delta-wye (Pi-Tee) equivalent circuit

21

Wheatstone Bridge Wheatstone Bridge

The Wheatstone bridge circuit is used to precisely measure resistance of medium values, that is in the range of 1Ω to 1MΩ.

The bridge circuit consists of four resistors, a dc voltage source and a detector.

22

2R1R

sV

XR3R

The Wheatstone bridge circuit:

Wheatstone Bridge Wheatstone Bridge

23

When the bridge is balanced:

2211

xx33

RiRi

RiRi

x2

31

ii

ii

Combining these equation, gives

x231 RiRi

Wheatstone BridgeWheatstone Bridge

24

Solving these equation, yields

31

2x

2

x

1

3

RR

RR

R

R

R

R

Wheatstone BridgeWheatstone Bridge

25

Series/parallel resistorSeries/parallel resistorVoltage divider circuitVoltage divider circuitCurrent divider circuitCurrent divider circuitVoltage and current Voltage and current

measurementmeasurementWheatstone bridgeWheatstone bridgeDelta-wye (Pi-Tee) equivalent Delta-wye (Pi-Tee) equivalent

circuitcircuit

RESISTIVE RESISTIVE CIRCUITCIRCUIT

26

Delta-Wye (PI-TEE) Delta-Wye (PI-TEE) CircuitCircuit

If the galvanometer in Wheatstone bridge is replace with its equivalent resistance Rm,

27

The resistor R1, R2 and Rm (or R3, Rm and Rx) are referred as a delta (∆) interconnection.

It is also referred as a pi (π) interconnection because the ∆ can be shaped into a π without disturbing the electrical equivalent of the two configurations.

28

Delta configuration

29

The resistors R1, Rm dan R3 (or R2, Rm and Rx) are referred as a wye (Y) interconnection because it can be shaped to look like the letter Y.

The Y configuration also referred as a tee (T) interconnection.

30

Wye configuration

31

The ∆ - Y The ∆ - Y Transformation Transformation

32

Using series and parallel simplifications in Δ-connected, yield

31

32

21

)(

)(

)(

RRRRR

RRRR

RRRRR

RRRR

RRRRR

RRRR

cba

acbca

cba

cbabc

cba

bacab

33

Using straightforward algebraic manipulation gives,

cba

ba

cba

ac

cba

cb

RRR

RRR

RRR

RRR

RRR

RRR

3

2

1

34

The expression for the three Δ-connected resistors as functions of three Y-connected resistors are

3

133221

2

133221

1

133221

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

c

b

a

35

Example #2Example #2 Find the current and power supplied by

the 40 V sources in the circuit shown below.

36

Solution: We can find this equivalent resistance

easily after replacing either the upper Δ (100Ω, 125Ω, 25Ω) or the lower Δ (40Ω, 25Ω, 37.5Ω) with its equivalent Y.

We choose to replace the upper Δ. Thus,

Example #2Example #2

37

10250

25100

5.12250

25125

50250

125100

1

2

1

R

R

R

Example #2Example #2

38

Substituting the Y-resistor into the circuit,

39

The equivalent circuit,

40

Calculate the equivalent resistance,

Simplify the circuit,

80100

505055eqR

41

Then, the current and power values are,

Wp

Ai

205.040

5.050

40

42

Example #3Example #3Find no load value of vo.Find vo when RL = 150 kΩHow much power is dissipated in the 25 kΩ

resistor if the load terminals are short-circuited ?

43

a)

b)

Vk

kv 150

100

752000

Vk

kv

kkk

kkReq

33.13375

50200

5015075

15075

0

Example #3Example #3

44

c)

W

RIp

AkR

VI

6.1

)108)(200(

10825

200

32

3

Example #3Example #3

45

Example #4Example #4 Find the power dissipated in the 6 Ω resistor.

46

Solution: Equivalent resistance

current io,

46.1)64(eqR

Ai 8416

16100

Example #4Example #4

47

Note that io is the current in the 1.6Ω resistor.

Use current divider to get current in the 6Ω resistor,

Then the power dissipated by the resistor is

Ai 2.310

486

WRIp 44.61)6()2.3( 22

Example #4Example #4

48

Example #5Example #5 Find the voltage of vo and vg.

49

Solution: Equivalent resistance

Current in resistor 30Ω

203060

Ai 15125

)75)(25(30

Example #5Example #5

50

Voltage v0

Total voltage at the resistor

Vv 300)20)(15(0

V

iv

750

45030030 300

51

Voltage vg

750)25(12 gv

Vvg 1050

52

Example #6Example #6 Find the current of ig and io in the circuit.

Solution: Equivalent resistance:

106484010

4205

53

The current values,

Thus,

Aig 5.1228

125

Ai 1050

)5.12)(40(6

Ai 225

)10)(5(0

Example #6Example #6

54

Example #7Example #7 Determine the value of io

55

Example #8Example #8 Find i and Vo

56

Example #9Example #9 Calculate the value of current; I.