Q 12-07-121JEE MainJEE Main 2021 (20 Jul, Shift 2)Medium
For a series LCR circuit with $R = 100\ \Omega$, $L = 0.5$ mH and $C = 0.1$ pF connected across 220 V - 50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is:
Answer: (D) ≈ 90°, predominantly capacitive circuit
$X_L = 2\pi\times50\times0.5\times10^{-3} \approx 0.16\ \Omega$
$X_C = \dfrac{1}{2\pi\times50\times0.1\times10^{-12}} \approx 3.2\times10^{10}\ \Omega$
$X_C \gg X_L, R$, so $\tan\phi = \dfrac{X_C - X_L}{R}$ is huge and $\phi \approx 90^\circ$: the circuit is predominantly capacitive.
Solution by Sreeraj P, M.Sc Physics