JEE Main 2025 — Alternating Current Question with Solution

To calculate the average power dissipated in the circuit, we follow these steps:

Formula for Power:

$P=V_{\text{rms}}\times I_{\text{rms}}\times \cos \varphi$

Expressing Power in Terms of Voltage and Impedance:

$P=V_{\text{rms}}\times \frac{V_{\text{rms}}}{Z}\times \frac{R}{Z}$

Simplifying the Expression:

$P=\frac{V_{\text{rms}}^2\times R}{Z^2}$

Calculate Impedance (Z):

The impedance of the circuit (Z) is calculated as:

$Z=\sqrt{R^2+(X_L-X_C{)}^2}$

Given:

- $X_L=100\Omega$

- $X_C=50\Omega$

- $R=50\Omega$

$X_L-X_C=100\Omega -50\Omega =50\Omega$

Thus:

$Z=\sqrt{50^2+50^2}=50\sqrt{2}\Omega$

Substitute Values to Find Power (P):

Given $V_{\text{rms}}=10\text{V}$, we calculate $P$ as follows:

$P=\frac{10^2\times 50}{(50\sqrt{2}{)}^2}$

Simplifying further:

$P=\frac{100\times 50}{2500\times 2}=1\text{W}$

Therefore, the average power dissipated by the circuit is $1\text{W}$.