02 AC Circuit Analysis1-Q&S

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EE2901S Basic Electricity & Electronics 1 AC Circuit Analysis: 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 I 3 at 60 Hz when I 1 = 630° A, I 2 = 220° A. Question 3 Find v(t) when i(t) = 10 cos (2t) A, R = 5 Ω, L = 5 H, C = 0.2 F. I 2 I 3 R 3 R 2 R 1 I 1 L C R i (t) v(t)

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02 AC Circuit Analysis1-Q&S.pd

Transcript of 02 AC Circuit Analysis1-Q&S

  • 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)

  • 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)

  • 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

  • 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)

  • 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

  • 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)

  • 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

  • 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

  • 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)

  • 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

  • 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

  • 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

  • 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