Q 12-07-054JEE MainJEE Main 2024 (6 Apr, Shift 1)Medium
When a dc voltage of $100\ \text{V}$ is applied to an inductor, a dc current of $5\ \text{A}$ flows through it. When an ac voltage of $200\ \text{V}$ peak value is connected to the inductor, its inductive reactance is found to be $20\sqrt3\ \Omega$. The power dissipated in the circuit is ______ W.
Numerical value type. Enter your answer.
Answer: 250
Resistance of the coil (from the dc test): $R = \dfrac{100}{5} = 20\ \Omega$.
$$Z = \sqrt{20^2 + (20\sqrt3)^2} = 40\ \Omega,\qquad I_{rms} = \frac{200/\sqrt2}{40} = \frac{5}{\sqrt2}\ \text{A}$$
$$P = I_{rms}^2R = \frac{25}{2}\times20 = 250\ \text{W}$$
Solution by Sreeraj P, M.Sc Physics