Match List - I with List - II.
| List - I | List - II |
| (A) The current lags behind the emf by \( \pi/4 \) in phase | (I) A.C. circuit containing only an inductor |
| (B) The e.m.f. lags behind the current by \( \pi/4 \) in phase | (II) A.C. circuit with resistance and inductances in series |
| (C) The current lags behind the e.m.f. in phase by \( \frac{\pi}{2} \) | (III) A.C. circuit containing only a capacitor |
| (D) The e.m.f. lags behind the current in phase by \( \frac{\pi}{2} \) | (IV) A.C. circuit with resistance and capacitor in series |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
The phase difference between current and emf in an ac circuit is set by the elements in it. In a pure inductor the current lags the emf by \( \pi/2 \); in a pure capacitor it leads by \( \pi/2 \). With a resistor in series the phase angle lies between 0 and \( \pi/2 \), given by
\( \displaystyle \tan\phi = \frac{X_L}{R} \quad \text{(L-R)} \qquad \tan\phi = \frac{X_C}{R} \quad \text{(C-R)} \)
(A) The current lags behind the emf by \( \pi/4 \) in phase — this matches (II) A.C. circuit with resistance and inductances in series. A lagging current means an inductive circuit, and a lag of less than \( \pi/2 \) needs a resistance too (here \( X_L = R \)).
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase — this matches (IV) A.C. circuit with resistance and capacitor in series. A leading current means a capacitive circuit, and a phase of less than \( \pi/2 \) needs a resistance in series (here \( X_C = R \)).
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \) — this matches (I) A.C. circuit containing only an inductor. Only a pure inductor makes the current lag by the full \( \pi/2 \).
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \) — this matches (III) A.C. circuit containing only a capacitor. Only a pure capacitor makes the current lead by the full \( \pi/2 \).