MCQ on Power of Alternating Current: Introduction & Explanation

Ans. (d). Changes constantly

Explanation: The direction of current in an AC circuit changes constantly. The voltage also reverses periodically in an AC circuit.

Ans. (a). 0

Explanation: For a pure inductor circuit, ϕ = 90° (∵ current lags the voltage by 90° in the pure inductive circuit)

Cos ϕ = Cos 90° = 0

P = V_rmsI_rms 0

P = 0 W

Ans. (b). 2.5 kW

Explanation: Here, potential difference (V) = 100 sint V and I = 100 sin (100t + \(\sqrt 2\)/3) A 

So, peak voltage (E_o) = 100, peak current (I_o) = 100 and phase difference (θ) = \(\sqrt 2\)/3

The average power loss in an AC circuit is given by;

P = V_rmsI_rmsCosθ

P = V_o/\(\sqrt 2\) I_o/\(\sqrt 2\) Cosθ

P = 100/\(\sqrt 2\)2 100/\(\sqrt 2\)2 cos \(\sqrt 2\)/3 

P = 2.5 x 10³ W 

P = 2.5 kW

Ans. (b). v_oi_o/4

Explanation: v = v_o sin (t)

i = i_o sin (t + \(\sqrt 2\)/3)

Phase difference (θ) = \(\sqrt 2\)/3

Peak current (I) = i_o

Peak voltage (V) = v_o

rms current (I_rms) = I/\(\sqrt 2\) = i_o/\(\sqrt 2\)

rms voltage (V_rms) = V/\(\sqrt 2\) = vo/\(\sqrt 2\)

P_avg = V_rmsI_rmsCosθ

Average power (P_avg) = v_o/\(\sqrt 2\) i_o/\(\sqrt 2\) Cos\(\sqrt 2\)/3

P_avg = v_oi_o/2 x ½ = v_oi_o/4

Ans. (a). 1000 W

Explanation: Given, R = 40 \(\Omega\), L = 30 H, C = 25\(\mu\)F and E_rms = 200 V

At resonance, X_L = X_C 

Z = \(\sqrt R ^2\) + \(\sqrt {(X_L - X_C)^2}\) = \(\sqrt 40 ^2\) = 40

Average power dissipated per cycle is,

P_av = E²_rms / Z = (200)2/40 = 1000 W

Ans. (c). 0.8

Explanation: R = 8\(\Omega\), XC = 25, XL = 31 and V = 110 V

Z = \(\sqrt R ^2\) + \(\sqrt {(X_L - X_C)^2}\) 

Z = \(\sqrt 8 ^2\) + \(\sqrt {(31 - 25)^2}\)  = \(\sqrt {(64+36)}\) 

Z = 10\(\Omega\)

The power factor (P) of a series LCR-circuit is given by, 

Cos ϕ = R/Z

Cos ϕ = 8/10 = 0.8

Ans. (b). Current, emf, and phase difference

Explanation: The average power dissipated in an LCR circuit is given by;

P_avg = V_rmsI_rmsCosθ

Thus, the average power depends upon current, emf, and phase difference.

Ans. (a). Power factor

Explanation: The power factor in an AC circuit is defined as the ratio of the actual power used by the circuit to the apparent power of the circuit. It is the amount by which power delivered in the circuit is less than the theoretical power of the circuit. Hence, it is a measure of loss of power in an AC circuit. 

Ans. (c). Magnitude and direction both

Explanation: In an alternating current, both the direction and the magnitude vary. The waveform of an AC power circuit is usually a sine wave. The sine wave oscillates periodically between positive and negative directions and leads to the most efficient transmission of energy. 

Ans. (b). 50 Hz

Explanation: In most European countries, the frequency of AC mains is 50 Hz. In the USA, it is 60 Hz. 

Ans. (a). 1/100 second

Explanation: The frequency of AC voltage in India is 50 Hz. It means 50 waves are produced in 1 second. In a single wave, the direction changes 2 times. Thus, in 50 waves direction will be changed, 50 2 = 100 times. 

This indicates that the direction is changed 100 times in 1 second. Thus, the direction is changed every 1/100 second.