JEE Main 2024 — Alternating Current Question with Solution

To determine the power dissipated in the circuit, follow these steps:

1. Calculate the resistance (R) using the DC current:

$R=\frac{100\text{V}}{5\text{A}}=20\Omega$

1. Determine the impedance (Z) by considering both resistance (R) and inductive reactance ($X_L$):

$Z=\sqrt{R^2+X_L^2}=\sqrt{20^2+(20\sqrt{3}{)}^2}=40\Omega$

1. Compute the peak current ($I_0$) using the AC peak voltage ($V_0$):

$I_0=\frac{V_0}{Z}=\frac{200\text{V}}{40\Omega }=5\text{A}$

1. Calculate the power (P) using the RMS values of voltage and current, and consider the phase angle ($\cos \varphi$):

$P=V_{\text{rms}}\cdot I_{\text{rms}}\cdot \cos \varphi =\frac{V_0\cdot I_0}{2}\times \frac{R}{Z}=\frac{200\cdot 5}{2}\times \frac{20}{40}=250\text{W}$