Series LCR Circuit question from JEE Main 2026 (2 Apr, Shift 2)

Answer: (b)

1. S1 shorts $L_2$ (leaves R, C, $L_1$); S2 shorts $L_1$ (leaves R, C, $L_2$). $X_C = \dfrac{1}{300 \times 10^{-4}} = \dfrac{100}{3}\ \Omega$.
2. S1 closed: $300L_1 - \dfrac{100}{3} = R\tan 30^\circ = \dfrac{R}{\sqrt{3}}$
3. S2 closed: $300L_2 - \dfrac{100}{3} = R\tan 60^\circ = \sqrt{3}R$
4. Second = 3 × first: $300L_2 - \dfrac{100}{3} = 900L_1 - 100 \Rightarrow 900L_1 - 300L_2 = \dfrac{200}{3}$
5. $3L_1 - L_2 = \dfrac{2}{9}\text{ H}$. So the answer is (b) $\dfrac{2}{9}$.