Q 12-07-074JEE MainJEE Main 2023 (31 Jan, Shift 1)Medium
An inductor of $0.5\ \text{mH}$, a capacitor of $20\ \mu\text{F}$ and resistance of $20\ \Omega$ are connected in series with a $220\ \text{V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt x$ A. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 242
In phase means resonance, so $Z=R=20\ \Omega$. Taking $220\ \text{V}$ as the rms value, the peak voltage is $220\sqrt2\ \text{V}$:
$$I_0=\frac{220\sqrt2}{20}=11\sqrt2=\sqrt{242}\ \text{A}$$
So $x=242$.
Solution by Sreeraj P, M.Sc Physics