Q 12-07-145JEE MainJEE Main 2019 (8 Apr, Shift 2)Easy
A circuit connected to an ac source of emf $e = e_0\sin(100t)$ with $t$ in seconds, gives a phase difference of $\dfrac\pi4$ between the emf $e$ and current $i$. Which of the following circuits will exhibit this?
Answer: (D) RC circuit with $R = 1\ \text{k}\Omega$ and $C = 10\ \mu\text{F}$
A phase difference of $\pi/4$ needs the reactance to equal the resistance, $X = R = 1000\ \Omega$, with $\omega = 100\ \text{rad/s}$.
RC: $\dfrac{1}{\omega C} = 1000 \Rightarrow C = \dfrac{1}{100\times1000} = 10\ \mu\text{F}$. This matches.
(RL would need $L = R/\omega = 10\ \text{H}$, which is not offered; $C = 1\ \mu\text{F}$ gives $X = 10\ \text{k}\Omega$.)
Solution by Sreeraj P, M.Sc Physics