Question 15

Match List-I with List-II:
List-I | List-II
a. Phase difference between current and voltage in a purely resistive AC circuit | i. $$\frac{\pi}{2}$$; current leads voltage
b. Phase difference between current and voltage in a pure inductive AC circuit | ii. zero
c. Phase difference between current and voltage in a pure capacitive AC circuit | iii. $$\frac{\pi}{2}$$; current lags voltage
d. Phase difference between current and voltage in an LCR series circuit | iv. $$\tan^{-1}\left(\frac{X_C - X_L}{R}\right)$$
Choose the most appropriate answer from the options given below:

Solution

In a purely resistive AC circuit, the current and voltage are in phase, so the phase difference is zero. This matches (a) with (ii).

In a purely inductive AC circuit, the current lags the voltage by $$\frac{\pi}{2}$$. This matches (b) with (iii).

In a purely capacitive AC circuit, the current leads the voltage by $$\frac{\pi}{2}$$. This matches (c) with (i).

In an LCR series circuit, the phase difference between current and voltage is $$\phi = \tan^{-1}\left(\frac{X_C - X_L}{R}\right)$$. This matches (d) with (iv).

Therefore the correct matching is (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv).

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