JEE Main 2005 — Alternating Current Question with Solution

The phase difference between the alternating current and emf in an AC circuit depends on the components in the circuit:

• In a purely resistive ($R$) circuit, the current and emf are in phase, meaning the phase difference is $0$.


• In a purely inductive ($L$) circuit, the current lags behind the emf by $\frac{\pi }{2}$, meaning the phase difference is $\frac{\pi }{2}$.


• In a purely capacitive ($C$) circuit, the current leads the emf by $\frac{\pi }{2}$, again meaning the phase difference is $\frac{\pi }{2}$.


• In an $L$-$R$ or $L$-$C$ circuit, the phase difference depends on the relative values of $L$, $R$, and $C$ and can be anywhere between $0$ and $\frac{\pi }{2}$.

Therefore, if the phase difference between the alternating current and emf is $\frac{\pi }{2}$, then the circuit cannot contain only a resistor ($R$) since that would give a phase difference of $0$. So, the answer is Option A: $R,L$. The phase difference would not be $\frac{\pi }{2}$ if the circuit contains both a resistor and an inductor.