02 ac circuit analysis1-q&s
DESCRIPTION
02 AC Circuit Analysis1-Q&S.pdTRANSCRIPT
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EE2901S Basic Electricity & Electronics 1
ACCircuitAnalysis:Questions
Question 1 An inductor draws a current of 5 A rms from a 110 V rms, 60 Hz voltage source. Express the instantaneous voltage and current mathematically. Question 2 Find I3 at 60 Hz when I1 = 630 A, I2 = 220 A.
Question 3 Find v(t) when i(t) = 10 cos (2t) A, R = 5 , L = 5 H, C = 0.2 F.
I2
I3 R3
R2
R1 I1
L C R i (t)
v(t)
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EE2901S Basic Electricity & Electronics 2
ACCircuitAnalysis:Questions
Question 4 Evaluate the current and voltage of each element. Draw a phasor diagram to show all the voltages and currents. It is given that VS = 173.2 V, R1 = 10 , R2 = 20 , C = -j11.55
Question 5 Determine the currents I1, I2, I3 and draw the phasor diagram for all currents when VS = 100 V, R1 = 2 , R2 = 3 , R3 = 5 , L1 = j3 , L2 = j5 , C1 = j6 . Question 6 Use the mesh-current method to find i1(t) and i2(t) when R1 = 75 , R2 = 100 , C = 1 F, L = 0.5 H, V (t)= 15cos(1500 t) V.
R2 C VS
R1 V1
I1 I2 I3
L1 C1
VS
R1
R2
R3
L2
I1
I2
I3
1 2 3
L
C R2
R1
V
i1(t) i2(t)
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EE2901S Basic Electricity & Electronics 3
ACCircuitAnalysis:Questions
Question 7 The power factor of a circuit is 0.866 lagging. If the input power is 600 W at a voltage
2 110 sin377 10 V, what is the instantaneous current i? Question 8 Given R1 = 4 , R2 = 10 , R3 = 3 , ZC = -j3 , ZL = j4 . a) Determine the phase currents Iab, Ibc, Ica as supplied by a
220 V, 3-phase source. b) Determine the line currents Ia, Ib, Ic. c) Verify that the phasor sum of the line currents is zero. d) Draw a phasor diagram showing Ia, Ib, Ic and Vab, Vbc, Vca.
Question 9 Determine the three ammeter readings for the circuit as supplied by a 3-phase, 240 V, 60 Hz source, provided that Za = 30 , Zb = 460 , Zc = 590 .
R3
C
R1
Vb
Ia Va
Vc
R2 Ib
Ic
IcaIab
Ibc
L
Ic
Vb
Ia Va
Vc
Ib
Za
Zb
Zc
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EE2901S Basic Electricity & Electronics 4
ACCircuitAnalysis:Solutions
Question 1 An inductor draws a current of 5 A rms from a 110 V rms, 60 Hz voltage source. Express the instantaneous voltage and current mathematically. Solution 1 2 377rad/s
25 7.07A
7.07 cos377 A
2110 155.56V
155.56cos377 90V ( Voltage leads current by 90 in an inductor)
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EE2901S Basic Electricity & Electronics 5
ACCircuitAnalysis:Solutions
Question 2 Find I3 at 60 Hz when I1 = 630 A, I2 = 220 A. Solution 2 I3 = I1 I2 = 630 220 = 6 (cos 30 + j sin 30) 2 (cos 20 + j sin 20) = (5.196 + j 3) (1.879 + j 0.684) = 3.317 + j 2.316 = 4.045 34.9 A
I2
I3 R3
R2
R1 I1
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EE2901S Basic Electricity & Electronics 6
ACCircuitAnalysis:Solutions
Question 3 Find v(t) when i(t) = 10 cos (2t) A, R = 5 , L = 5 H, C = 0.2 F. Solution 3 = 2 rad/s I = 100 A ZL = jL = j 10
1
2.5
1
1
1
1
1
15
110
12.5
1
0.2 0.3 1.54 2.31 2.78 56.3
V = I Zeq = (100) (2.78 56.3) = 27.856.3 V v(t) = 27.8 cos (2t - 56.31) V
L C R i (t)
v(t)
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EE2901S Basic Electricity & Electronics 7
ACCircuitAnalysis:Solutions
Question 4 Evaluate the current and voltage of each element. Draw a phasor diagram to show all the voltages and currents. It is given that VS = 173.2 V, R1 = 10 , R2 = 20 , C = -j11.55 Solution 4 For Node 1,
173.2
10 20
11.55
0
100 30V Thus, we have
100 30V
173.2 10030A
1010030
10 1030A
20100 30
20 5 30A
11.55
100 30
11.55 90 8.6660A
R2 C VS
R1 V1
I1 I2 I3
VR1
VS
V1
I1
I3
30 60
-30
I2
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EE2901S Basic Electricity & Electronics 8
ACCircuitAnalysis:Solutions
Question 5 Determine the currents I1, I2, I3 and draw the phasor diagram for all currents when VS = 100 V, R1 = 2 , R2 = 3 , R3 = 5 , L1 = j3 , L2 = j5 , C1 = j6 . Solution 5
2 3 3 55 6
3 5 5 6
2 3 5.82597.81 50.2
8.06 7.12
2 j3 5.6515.92 7.43 4.55 8.7131.48
100
8.7131.48 11.48 31.48A
11.48 31.485.6515.92 64.86 15.56V
64.86 15.56
3 564.86 15.56
5.8359 11.12 74.56A
64.86 15.56
5 664.86 15.56
7.81 50.19 8.334.63A
L1 C1
VS
R1
R2
R3
L2
I1
I2
I3
1 2 3
I2
I1
VS -31.48
34.63
-74.56
I3
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EE2901S Basic Electricity & Electronics 9
ACCircuitAnalysis:Solutions
Question 6 Use the mesh-current method to find i1(t) and i2(t) when R1 = 75 , R2 = 100 , C = 1 F, L = 0.5 H, V (t)= 15cos(1500 t) V. Solution 6
15001 10 666.7
15000.5 750 For Mesh 1, R1 I1 + ZC (I1 I2) V = 0 For Mesh 2, ZC (I2 I1) + (R2 + ZL) I2 = 0 These are: 75 666.7 15 0
666.7 100 750 0 Solving above equations, we have
I1 = 3.810-3 46.6 A I2 = 19.610-3 83.2 A
i1(t) = 3.8 10-3 cos (1500t + 46.6) A i2(t) = 19.610-3 cos (1500t 83.2) A
L
C R2
R1
V
i1(t) i2(t)
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EE2901S Basic Electricity & Electronics 10
ACCircuitAnalysis:Solutions
Question 7 The power factor of a circuit is 0.866 lagging. If the input power is 600 W at a voltage
2 110 sin377 10 V, what is the instantaneous current i? Solution 7
cos 0.866lagging cos0.866 30lagging
cos
600 1100.866
600
1100.866 6.3A
6.32 8.9A
Now, 30 lagging implies that i lags v by30. Hence, 8.9 sin377 20 A
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EE2901S Basic Electricity & Electronics 11
ACCircuitAnalysis:Solutions
Question 8 Given R1 = 4 , R2 = 10 , R3 = 3 , ZC = -j3 , ZL = j4 . a) Determine the phase currents Iab, Ibc, Ica as supplied by a
220 V, 3-phase source. b) Determine the line currents Ia, Ib, Ic. c) Verify that the phasor sum of the line currents is zero. d) Draw a phasor diagram showing Ia, Ib, Ic and Vab, Vbc, Vca.
Solution 8 (a)
2200
4 3
2200
5 36.87 4436.87A
220 120
3 4220 120
553.13 44 173.13A
220120
100 22120A
(b) 4436.87 22120 46.2 7.35 46.789A
44 173.13 4436.87 78.88 31.66 85 158A 22120 44 173.13 32.68 24.31 40.7336.6A
R3
C
R1
Vb
Ia Va
Vc
R2 Ib
Ic
IcaIab
Ibc
L
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EE2901S Basic Electricity & Electronics 12
c 46.789 46.2 7.35A
85 158 78.88 31.66A 40.7336.6 32.68 24.31A
, , 0 0
(d)
Vbc
Ia
Vca
Ic
Ib
120
9
36.6
Vab
158 120
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EE2901S Basic Electricity & Electronics 13
ACCircuitAnalysis:Solutions
Question 9 Determine the three ammeter readings for the circuit as supplied by a 3-phase, 240 V, 60 Hz source, provided that Za = 30 , Zb = 460 , Zc = 590 . Solution 9 The two mesh equations are
30 460
460 590 The equations become
2400 6.0834.72 460240 120 4 120 8.69776.7
SolvingforI1andI2,wehave
I1 = 41.24-55.88 and I2 = 22.68-152.90 Referring to circuit, we have
41.24 55.88
22.6827.1 22.6827.1 41.24 55.88 49.76150.95
Ic
Vb
Ia
Va
Vc
Ib
Za
Zb
Zc
Ic
Vb
Ia
Va
Vc
Ib
Za
Zb
Zc
I1
I2