Upload
carmella-hawkins
View
219
Download
1
Tags:
Embed Size (px)
Citation preview
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.