Question

When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be \( 20\sqrt{3} \, \Omega \). The power dissipated in the circuit is _________ W.

Answer 1

Correct Answer: 250

For DC voltage:

\[ R = \frac{V}{I} = \frac{100}{5} = 20 \, \Omega \]

For AC voltage:

\[ X_L = 20\sqrt{3} \, \Omega \]

\[ Z = \sqrt{X_L^2 + R^2} = \sqrt{(20\sqrt{3})^2 + 20^2} = \sqrt{1200 + 400} = 40 \, \Omega \]

Power dissipated in the circuit:

\[ P = I_\text{rms}^2 R = \left( \frac{V_\text{rms}}{Z} \right)^2 \times R \]

\[ P = \left( \frac{200}{\sqrt{2} \times 40} \right)^2 \times 20 \]

\[ P = \left( \frac{200}{40\sqrt{2}} \right)^2 \times 20 = 250 \, \text{W} \]