and 75.8 μF capacitor.

Determine the voltage drop

across the capacitor of the circuit.
A. 50 V B. 87 V C. 100 V D. 350 V

11. A circuit consisting of a choking coil having an

inductance of 0.05 H and a resistance of 10 Ω is
connected to a 200 V rms supply at a frequency of
50 Hz and having a sine – wave shape. Estimate the
average power expanded in the circuit.
PROBLEM SETS IN AC CIRCUITS A. 1,160 W C. 1,180 W
B. 1,170 W D. 1,190 W
1. An e.m.f. e1 = 50 sin ωt and an e.m.f. e2 = 30 sin (ωt
– π/6) act together in the same circuit. Find the 12. A circuit combining a resistance of 20 Ω, an
resultant e.m.f. inductance of 0.1 H and a 100 μF capacitor all
A. 47.5 sin (ωt – 11°10’) connected in series across 220 V, 60 Hz supply. Find
B. 57.5 sin (ωt – 11°10’) the total power factor.
C. 67.5 sin (ωt – 11°10’) A. 0.823 lagging C. 0.873 lagging
D. 77.5 sin (ωt – 11°10’) B. 0.833 leading D. 0.883 leading

2. Current flows through a circuit consisting of 13. Find the value of impedance of the circuit which
impedances AB and BC. The current lags by 30° requires power of 1,540 VAR, voltage of 230 V and
behind the voltage of 150 V between A and B and current of 10 A.
leads by 50° on the voltage of 180 V between B and A. 17.08 + j15.40 Ω C. 15.40 + j17.08 Ω
C. Find the resultant voltage between A and C. B. 27.43 – j12.45 Ω D. 20.56 – j18.92 Ω
A. 234 V C. 254 V
B. 244 V D. 264 V 14. A coil with resistance is placed in series with non –
inductive resistance of 3 Ω. When a voltage of 104 V
3. If the voltage represented by V = 140 sin ωt is is applied to the circuit, the voltage across the coil is
connected to a non-inductive resistance of 8 Ω, 66 V and that across the resistor 50 V. Calculate the
calculate the maximum value of the current. The power factor of the coil.
frequency of the applied voltage is 50 Hz. A. 0.5 B. 0.6 C. 0.7 D. 0.8
A. 13.5 A B. 17.5 A C. 15.5 A D. 19.5 A
15. When a DC voltage of 30 V is applied to a given coil,
4. A coil of negligible resistance has an inductance of the power consumed is 150 W. When an AC voltage
0.01 H. A voltage represented by 140 sin ωt is of 230 V rms is applied to the same coil, the power
applied to it, the frequency being 50 Hz. Calculate consumed is 3,174 W. Find the reactance of the coil.
the current flowing through the coil. A. 6 Ω B. 8 Ω C. 12 Ω D. 15 Ω
A. 42.5 sin (ωt – π/2) A
B. 44.5 sin (ωt – π/2) A 16. Consider a series RLC circuit with R = 25 Ω, L = 6
C. 46.5 sin (ωt – π/2) A mH, and C = 25 μF. The circuit is connected to a 10
D. 48.5 sin (ωt – π/2) A V rms, 600 Hz AC source. Find the average power
delivered to the circuit.
5. A voltage represented by 150 sin ωt is applied to a A. 2.4 W B. 3.2 W C. 4.8 W D. 6.4 W
capacitor of capacitance 24 μF. The frequency is 25
Hz. Calculate the maximum value of current. 17. A coil having an impedance of 25 Ω and a resistance
A. 0.266 A C. 0.366 A of 15 Ω is connected in parallel with a non – inductive
B. 0.466 A D. 0.566 A resistance of 10 Ω. Calculate the total admittance.
A. 0.124 S C. 0.128 S
6. A voltage represented by 280 sin ωt is applied to a B. 0.132 S D. 0.136 S
coil having a resistance of 20 Ω and an inductance of
0.02 H. The frequency is 50 Hz. Find the phase 18. A piece of equipment consumes 2,000 W when
difference between the voltage and the current. supplied with 110 V and takes a lagging current of 25
A. 17°26’ C. 22°26’ A. If a capacitor is connected in parallel with the
B. 27°26’ D. 32°26’ equipment to make the power factor unity, find its
capacitance. The supply frequency is 100 Hz.
7. A choking coil takes 10 A when connected to an A.C. A. 218 μF C. 238 μF
supply of 230 V, 50 Hz. If the resistance of the coil is B. 228 μF D. 248 μF
2 Ω, find its inductance.
A. 0.033 H C. 0.073 H 19. A coil of resistance 10 Ω and inductance 0.02 H is
B. 0.053 H D. 0.093 H placed in parallel with a 100 μF capacitor across a
200 – V rms, 50 Hz sinusoidal supply. Find the total
8. A coil of resistance 1 Ω and impedance 8.06 Ω is current supplied of the arrangement.
placed in series with a second coil of resistance 1.24 A. 12.57 A C. 14.57 A
Ω. When a voltage of 200 V is applied to the circuit, B. 13.57 A D. 15.57 A
the current flowing is 6.3 A. Find the inductance of
the second coil. The frequency of the supply is 50 For items 20 and 21
Hz. Three circuits A, B and C are connected in parallel across a
A. 0.025 H C. 0.075 H 200 V AC supply. Circuit A consists of a bank of lamps taking
B. 0.055 H D. 0.105 H a current of 10 A at unity power factor, B consists of an
inductive resistor taking a current of 20 A at a power factor of
9. A 255 V, 50 Hz supply is connected in series with a 0.8 and C consists of a resistor and capacitor in series taking
100 Ω resistor and a 2 μF capacitor. Taking the a current of 10 A at a power factor of 0.9.
phase of the emf as a reference, find the rms value 20. Find the power supplied to the whole circuit.
of the current in the circuit. A. 3,500 W C. 4,500 W
A. 0.16 A B. 0.32 A C. 0.24 A D. 0.40 A B. 7,000 W D. 9,000 W

10. Let an alternating rms voltage of 100 V at a 21. Calculate the power factor of the whole circuit.
frequency of 60 cycles per second be impressed on A. 0.877 leading C. 0.977 leading
a series circuit of 8.66 Ω resistor, 0.106 H inductor B. 0.877 lagging D. 0.977 lagging
 22. It is desired to transfer maximum power to the load Z 32. The current will lag the voltage when _____ is
in the given circuit. Find the maximum power if is = 5 present in the circuit.
cos 40t A. A. capacitance C. reluctance
A. 35 mW C. 55 mW B. inductance D. resistance
B. 75 mW D. 95 mW
33. The current will lead the voltage when _____.
A. inductive reactance exceeds the capacitive
reactance in the circuit
B. reactance exceeds the resistance in the circuit
C. resistance exceeds the reactance in the circuit
D. capacitive reactance exceeds the inductive
reactance in the circuit

34. For voltage and current to be in phase, _____.

A. the circuit impedance has only resistance
23. A resistance coil of 100 Ω has an inductance of 20 B. the voltage and current appear at their zero and
mH. What value of the effective self – capacitance peak values at the same time
would make it accurately non – inductive at a C. both A and B
frequency of 50 Hz? D. none of these
A. 100 μF C. 400 μF
B. 200 μF D. 500 μF 35. If the resistance in a series RC circuit is increased
the magnitude of the phase angle.
A circuit consisting of a coil having an inductance of 0.25 H A. Increases
and a resistance of 3 Ω is arranged in series with a capacitor B. Remains the same
of capacitance 20 μF. C. Decreases
24. Calculate at what frequency resonance will take D. Changes in an indeterminate manner
place if an alternating voltage of 40 V is applied to
the circuit. 36. In an AC circuit a value of watts divided by a value of
A. 63.2 Hz C. 71.2 Hz volt-amps, which of the following indicates close to
B. 82.4 Hz D. 92.6 Hz unity?
A. maximum current for the load
25. Find the voltage across the capacitor B. high power factor
A. 1,291 V C. 1,491 V C. maximum voltage for the load
B. 1,391 V D. 1,591 V D. low power factor

26. The AC system is preferred to the DC system 37. Reactance will cause the current in a circuit to vary
because _____. only when _____.
A. DC voltage cannot be used for domestic A. AC current flows
appliances B. DC current flows
B. DC motors do not have speed control C. there is no resistance in the circuit
C. AC voltages can be easily changed in D. there is resistance in the circuit
magnitude
D. high-voltage AC transmission is less efficient 38. Power absorbed in a pure inductive circuit is zero
because _______.
27. Which of the following is not true about the A. reactive component of current is zero
alternating current? B. active component of current is maximum
A. Develops eddy current C. power factor of the circuit is zero
B. It can be transformed D. reactive and active components of current cancel
C. Is suitable for charging batteries out
D. Interferes with communication lines
39. One of the reasons for improving the power factor is?
28. 60 cycle frequency travels 180 degrees in how many A. To avoid poor voltage regulation constant
seconds? B. To keep voltage regulation constant
A. 1/60 C. 1/180 C. To increase the voltage regulation
B. 1/120 D. 1/30 D. All of these

29. The r.m.s. value of sinusoidally varying current is 40. At series resonance, ____________.
________ that of its average value. A. circuit impedance is very large
A. more than B. circuit power factor is minimum
B. less than C. voltage across L or C is zero
C. same as D. circuit power factor is unity
D. none of these

30. Impedance of an a.c. circuit is a ___________.

A. phasor
B. vector quantity
C. scalar quantity
D. none of the above

31. In the impedance triangle the inductive reactance

and impedance phasor are analogous to the _____
and _____ phasor respectively in the voltage triangle.
A. Inductive voltage, total voltage
B. Inductive current , total current
C. Inductive voltage, resistive current
D. Inductive current, resistive current