Q 12-07-118JEE MainJEE Main 2021 (25 Feb, Shift 1)Medium
The angular frequency of alternating current in a L-C-R circuit is $100\ \text{rad s}^{-1}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.
Answer: (D) 0.8 H and 250 $\mu$F
The branch containing $R'$ has an open key, so it carries no current; the same current flows through $R$, $C$ and the coil.
$$I = \frac{V_R}{R} = \frac{15}{60} = 0.25\ \text{A}$$
$$X_L = \frac{20}{0.25} = 80\ \Omega \Rightarrow L = \frac{80}{100} = 0.8\ \text{H}$$
$$X_C = \frac{10}{0.25} = 40\ \Omega \Rightarrow C = \frac{1}{100\times40} = 250\ \mu\text{F}$$
Solution by Sreeraj P, M.Sc Physics