Q 12-07-037JEE MainJEE Main 2026 (4 Apr, Shift 1)Easy
An inductor of $10$ mH, capacitor of $0.1\,\mu$F and a resistor of $100\ \Omega$ are connected in series across an a.c power supply $220$ V, $70$ Hz. The power factor of the given circuit is $0.5$. The difference in the inductive reactance and capacitance reactance is $\sqrt{3}\alpha\,\Omega$. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 100
Concept. Power factor $\cos\phi = 0.5$ gives $\phi = 60°$, and $\tan\phi = \dfrac{|X_L - X_C|}{R}$.
Step 1. Phase. $\tan60° = \sqrt3$.
Step 2. Reactance difference. $|X_L - X_C| = \sqrt3 \times 100\ \Omega$, so $\alpha = 100$. (The given $L$, $C$ and frequency are not needed.)
Answer. $100$.
Solution by Sreeraj P, M.Sc Physics
