UNIT 2
A.C. Circuits
Que1) For a series RLC circuit having R=10ohms, L= 0.15H, C=100
F. They are connected across 100v 50Hz supply. Calculate total impedance?
Sol: Impedance Z= 
Z= 
= 18.27ohm
Que2) For a series RLC circuit having R=12ohms, L= 0.2H, C=60
F. They are connected across 100v 50Hz supply. Calculate circuit current?
Sol: I= 
Z= 
Z= 
= 13.89ohm
I = 100/13.89 =7.2A
Que3) For a series RLC circuit having R=10ohms, L= 0.15H, C=100
F. They are connected across 100v 50Hz supply. Calculate power factor?
Sol: cosφ = 
Impedance Z= 
Z= 
= 18.27ohm
Cosφ = 
= 
φ = 56.81o lagging
Que4) A coil takes a current of 6A when connected to 24V dc supply. To obtain the same current with 50HZ ac, the voltage required was 30V. Calculate inductance and p.f of coil?
Sol: The coil will offer only resistance to dc voltage and impedance to ac voltage
R =24/6 = 4ohm
Z= 30/6 = 5ohm
XL = 
= 3ohm
Cosφ = 
= 4/5 = 0.8 lagging
Que5) The potential difference measured across a coil is 4.5V,when it carries a dc current of 8A. The same coil when carries ac current of 8A at 25Hz,the potential difference is 24V. Find current and power when supplied by 50V,50Hz supply?
Sol: R=V/I= 4.5/8 = 0.56ohm
At 25Hz Z= V/I=24/8 =3ohm
XL = 
= 2.93ohm
XL = 2
fL = 2
x 25x L = 2.93
L=0.0187ohm
At 50Hz
XL = 2x3 =6ohm
Z = 
= 5.97ohm
I= 50/5.97 = 8.37A
Power = I2R = 39.28W
Que6) A coil having inductance of 50mH an resistance 10ohmis connected in series with a 25
F capacitor across a 200V ac supply. Calculate resonant frequency and current flowing at resonance?
Sol: f0=
= 142.3Hz
I0 = V/R = 200/10 = 20A
Que7) A 15mH inductor is in series with a parallel combination of 80ohm resistor and 20
F capacitor. If the angular frequency of the applied voltage is 1000rad/s find admittance?
Sol: XL = 2
fL = 1000x15x10-3 = 15ohm
XL = 1/
C = 50ohm
Impedance of parallel combination Z = 80||-j50 = 22.5-j36
Total impedance = j15+22.5-j36 = 22.5-j21
Admittance Y= 1/Z = 0.023-j0.022 siemens
Que8) A circuit connected to a 100V, 50 Hz supply takes 0.8A at a p.f of 0.3 lagging. Calculate the resistance and inductance of the circuit when connected in series and parallel?
Sol: For series Z =100/0.8 = 125ohm
Cosφ = 
R = 0.3 x 125 = 37.5ohm
XL = 
= 119.2ohm
XL = 2
fL = 2
x 50x L
119.2 = 2
x 50x L
L= 0.38H
For parallel:
Active component of current = 0.8 cosφ = 0.3x0.3 = 0.24A
R = 100/0.24 =416.7ohm
Quadrature component of current = 0.8 sinφ = 0.763
XL= 100/0.763 = 131.06ohm
L= 100/0.763x2
x50 = 0.417H
Que9) Calculate impedance of a parallel tuned RC circuit at a frequency of 400kHz and for a BW of operation equal to 20kHz. Given R=5ohm?
Sol: BW =R/2
L
L= 39
H
f0 = 
C = 2.6x10-9F
Z= L/RC = 3kohm
Q10) Three similar resistors are connected in star across 400V 3-phase lines. Line current is 4A. Calculate the value of each resistor.
Sol: For star connection:
IL=Iph=4A
Vph=VL/
= 400/
= 231V
Rph= 231/4= 57.75ohm
For Delta Connection:
IL=4A
Iph= IL/
=4/
==2.30A
Zph=400/2.30=173.9ohm
Rph= 173.9/3 = 57.97ohm
Q11) Three identical impedances are connected in delta 3-phase supply of 400V. The line current is 30A and total power taken from the supply is 10kW. Calculate the resistance and reactance value of each impedance?
Sol: VL=Vph=400V
IL=30A
Iph=IL/
= 30/
=17.32A
Zph=Vph/Iph= 400/17.32=23.09ohm
P=
VLIL Cos Ø
Cos Ø = 10000/
400x30 = 0.48
Sin Ø =0.88
Rph=Zph Cos Ø= 23.09x0.48=11.08ohm
Xph=Zph Sin Ø = 23.09x0.88=20.32ohm
Q12) A star connected alternator supplies a delta connected load. The impedance of the load branch is 6+j5 ohm/phase. The line voltage is 230V. Determine the current in the load branch and power consumed by the load.
Sol: Zph=
= 7.8ohm
VL=Vph=230V
Iph=Vph/Zph=230/7.8=29.49A
Iph=IL/
IL= 
Iph=
x29.49=51.07A
P=
VLIL Cos Ø = 
x 230x51.07x0.768=15.62kW
Q13) The load connected to a 3-phase supply comprise three similar coils connected in star. The line currents are 25A and the kVA and kW inputs are 18 and 10 respectively. Find the line and phase voltage, the kVAR input resistance and reactance of each coil?
Sol: IL= 25A
P= 10000W
Cos Ø = 10/18 = 0.56
P=
VLIL Cos Ø
10000=
x VLx25x0.56
VL =412.39V
Vph= VL/
= 412.39/
=238.09V
KVAR=
= 14.96
Zph=238.09/25=9.52ohm
Rph=Zph Cos Ø= 9.52x0.56=5.33ohm
Xph=Zph Sin Ø = 9.52x0.83=7.88ohm
Q14) A balanced delta connected load consisting of three coils draws 8
A at 0.5 p.f from 100V 3-phase ac supply. If the coils are reconnected in star across the same supply. Find the line current and total power consumed?
Sol: For Delta connection:
IL=8
A
Iph= IL/
= 8A
Vph=100V
Zph=100/8=12.5ohm
Rph=Zph Cos Ø=12.5x0.5 = 6.25ohm
Xph=Zph Sin Ø = 12.5x0.866=10.825ohm
P=
VLIL Cos Ø
= 
x 100x 8
x0.5=1200W
For Star Connection:
Vph= VL/
= 100/
V=57.73V
Zph=100/8=12.5ohm
Iph=57.73/12.5=4.62A
P=
VLIL Cos Ø
=
x 100x 4.62x0.5
P= 400W
UNIT 2
A.C. Circuits
Que1) For a series RLC circuit having R=10ohms, L= 0.15H, C=100
F. They are connected across 100v 50Hz supply. Calculate total impedance?
Sol: Impedance Z= 
Z= 
= 18.27ohm
Que2) For a series RLC circuit having R=12ohms, L= 0.2H, C=60
F. They are connected across 100v 50Hz supply. Calculate circuit current?
Sol: I= 
Z= 
Z= 
= 13.89ohm
I = 100/13.89 =7.2A
Que3) For a series RLC circuit having R=10ohms, L= 0.15H, C=100
F. They are connected across 100v 50Hz supply. Calculate power factor?
Sol: cosφ = 
Impedance Z= 
Z= 
= 18.27ohm
Cosφ = 
= 
φ = 56.81o lagging
Que4) A coil takes a current of 6A when connected to 24V dc supply. To obtain the same current with 50HZ ac, the voltage required was 30V. Calculate inductance and p.f of coil?
Sol: The coil will offer only resistance to dc voltage and impedance to ac voltage
R =24/6 = 4ohm
Z= 30/6 = 5ohm
XL = 
= 3ohm
Cosφ = 
= 4/5 = 0.8 lagging
Que5) The potential difference measured across a coil is 4.5V,when it carries a dc current of 8A. The same coil when carries ac current of 8A at 25Hz,the potential difference is 24V. Find current and power when supplied by 50V,50Hz supply?
Sol: R=V/I= 4.5/8 = 0.56ohm
At 25Hz Z= V/I=24/8 =3ohm
XL = 
= 2.93ohm
XL = 2
fL = 2
x 25x L = 2.93
L=0.0187ohm
At 50Hz
XL = 2x3 =6ohm
Z = 
= 5.97ohm
I= 50/5.97 = 8.37A
Power = I2R = 39.28W
Que6) A coil having inductance of 50mH an resistance 10ohmis connected in series with a 25
F capacitor across a 200V ac supply. Calculate resonant frequency and current flowing at resonance?
Sol: f0=
= 142.3Hz
I0 = V/R = 200/10 = 20A
Que7) A 15mH inductor is in series with a parallel combination of 80ohm resistor and 20
F capacitor. If the angular frequency of the applied voltage is 1000rad/s find admittance?
Sol: XL = 2
fL = 1000x15x10-3 = 15ohm
XL = 1/
C = 50ohm
Impedance of parallel combination Z = 80||-j50 = 22.5-j36
Total impedance = j15+22.5-j36 = 22.5-j21
Admittance Y= 1/Z = 0.023-j0.022 siemens
Que8) A circuit connected to a 100V, 50 Hz supply takes 0.8A at a p.f of 0.3 lagging. Calculate the resistance and inductance of the circuit when connected in series and parallel?
Sol: For series Z =100/0.8 = 125ohm
Cosφ = 
R = 0.3 x 125 = 37.5ohm
XL = 
= 119.2ohm
XL = 2
fL = 2
x 50x L
119.2 = 2
x 50x L
L= 0.38H
For parallel:
Active component of current = 0.8 cosφ = 0.3x0.3 = 0.24A
R = 100/0.24 =416.7ohm
Quadrature component of current = 0.8 sinφ = 0.763
XL= 100/0.763 = 131.06ohm
L= 100/0.763x2
x50 = 0.417H
Que9) Calculate impedance of a parallel tuned RC circuit at a frequency of 400kHz and for a BW of operation equal to 20kHz. Given R=5ohm?
Sol: BW =R/2
L
L= 39
H
f0 = 
C = 2.6x10-9F
Z= L/RC = 3kohm
Q10) Three similar resistors are connected in star across 400V 3-phase lines. Line current is 4A. Calculate the value of each resistor.
Sol: For star connection:
IL=Iph=4A
Vph=VL/
= 400/
= 231V
Rph= 231/4= 57.75ohm
For Delta Connection:
IL=4A
Iph= IL/
=4/
==2.30A
Zph=400/2.30=173.9ohm
Rph= 173.9/3 = 57.97ohm
Q11) Three identical impedances are connected in delta 3-phase supply of 400V. The line current is 30A and total power taken from the supply is 10kW. Calculate the resistance and reactance value of each impedance?
Sol: VL=Vph=400V
IL=30A
Iph=IL/
= 30/
=17.32A
Zph=Vph/Iph= 400/17.32=23.09ohm
P=
VLIL Cos Ø
Cos Ø = 10000/
400x30 = 0.48
Sin Ø =0.88
Rph=Zph Cos Ø= 23.09x0.48=11.08ohm
Xph=Zph Sin Ø = 23.09x0.88=20.32ohm
Q12) A star connected alternator supplies a delta connected load. The impedance of the load branch is 6+j5 ohm/phase. The line voltage is 230V. Determine the current in the load branch and power consumed by the load.
Sol: Zph=
= 7.8ohm
VL=Vph=230V
Iph=Vph/Zph=230/7.8=29.49A
Iph=IL/
IL= 
Iph=
x29.49=51.07A
P=
VLIL Cos Ø = 
x 230x51.07x0.768=15.62kW
Q13) The load connected to a 3-phase supply comprise three similar coils connected in star. The line currents are 25A and the kVA and kW inputs are 18 and 10 respectively. Find the line and phase voltage, the kVAR input resistance and reactance of each coil?
Sol: IL= 25A
P= 10000W
Cos Ø = 10/18 = 0.56
P=
VLIL Cos Ø
10000=
x VLx25x0.56
VL =412.39V
Vph= VL/
= 412.39/
=238.09V
KVAR=
= 14.96
Zph=238.09/25=9.52ohm
Rph=Zph Cos Ø= 9.52x0.56=5.33ohm
Xph=Zph Sin Ø = 9.52x0.83=7.88ohm
Q14) A balanced delta connected load consisting of three coils draws 8
A at 0.5 p.f from 100V 3-phase ac supply. If the coils are reconnected in star across the same supply. Find the line current and total power consumed?
Sol: For Delta connection:
IL=8
A
Iph= IL/
= 8A
Vph=100V
Zph=100/8=12.5ohm
Rph=Zph Cos Ø=12.5x0.5 = 6.25ohm
Xph=Zph Sin Ø = 12.5x0.866=10.825ohm
P=
VLIL Cos Ø
= 
x 100x 8
x0.5=1200W
For Star Connection:
Vph= VL/
= 100/
V=57.73V
Zph=100/8=12.5ohm
Iph=57.73/12.5=4.62A
P=
VLIL Cos Ø
=
x 100x 4.62x0.5
P= 400W
