Q 12-07-051JEE MainJEE Main 2024 (5 Apr, Shift 1)Medium
An ac source is connected in the given series LCR circuit. The rms potential difference across the capacitor of $20\ \mu\text{F}$ is ______ V.
Numerical value type. Enter your answer.
Answer: 50
$\omega = 100\ \text{rad/s}$: $X_L = \omega L = 100\ \Omega$, $X_C = \dfrac{1}{\omega C} = \dfrac{1}{100\times20\times10^{-6}} = 500\ \Omega$.
$$Z = \sqrt{300^2 + (500 - 100)^2} = 500\ \Omega,\qquad I_{rms} = \frac{50}{500} = 0.1\ \text{A}$$
$$V_C = I_{rms}X_C = 0.1\times500 = 50\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics