Match the LIST-I with LIST-II
| LIST-I (ac Circuits) | LIST-II (Phase relationships between current and voltage) | ||
|---|---|---|---|
| A. | Purely resistive circuit \((X_C - X_L = 0)\) | I. | Current lags or leads the voltage in phase |
| B. | Purely capacitive circuit \((X_L = 0, R = 0)\) | II. | Current lags the voltage by \(\pi/2\) |
| C. | Purely inductive circuit \((X_C = 0, R = 0)\) | III. | Current leads the voltage by \(\pi/2\) |
| D. | LCR circuit \((X_L \ne X_C)\) | IV. | Voltage and current are in phase |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-IV, B-III, C-II, D-I
The phase between current and voltage is set by the net reactance \( X_L - X_C \) compared with R: \( \tan\phi = (X_L - X_C)/R \).
(A) Purely resistive circuit \( (X_C - X_L = 0) \) — this matches (IV) Voltage and current are in phase. With no net reactance, \( \phi = 0 \).
(B) Purely capacitive circuit \( (X_L = 0, R = 0) \) — this matches (III) Current leads the voltage by \( \pi/2 \). The current is greatest when the capacitor is charging fastest, a quarter cycle before the voltage peaks.
(C) Purely inductive circuit \( (X_C = 0, R = 0) \) — this matches (II) Current lags the voltage by \( \pi/2 \). The self-induced emf of the inductor delays the growth of the current.
(D) LCR circuit \( (X_L \ne X_C) \) — this matches (I) Current lags or leads the voltage in phase. The current lags when \( X_L \gt X_C \) and leads when \( X_C \gt X_L \), by an angle between 0 and \( \pi/2 \).
NCERT (2026-27):
AC Voltage Applied to a Resistor – “… Clearly, the voltage and current are in phase with each other.”
AC Voltage Applied to a Capacitor – “… Thus, we see that in the case of an inductor, the current lags the voltage by \( \pi/2 \) and in the case of a capacitor, the current leads the voltage by \( \pi/2 \).”
Phasor-Diagram Solution – “… If \( X_C \gt X_L \), \( \phi \) is positive and the circuit is predominantly capacitive. Consequently, the current in the circuit leads the source voltage. If \( X_C \lt X_L \), \( \phi \) is negative and the circuit is predominantly inductive. Consequently, the current in the circuit lags the source voltage.”