An inductor of reactance 100Ω and resistor of resistance 100Ω are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 242 W
In a series LR circuit the average power is \( P = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi \), where \( \cos\phi = R/Z \). Only the resistor dissipates power; the inductor stores and returns energy.
\( Z = \sqrt{R^{2}+X_L^{2}} = \sqrt{100^{2}+100^{2}}\,\Omega \approx 141.4\,\Omega \)
\( \displaystyle I_{\mathrm{rms}} = \frac{V_{\mathrm{rms}}}{Z} = \frac{220\,\mathrm{V}}{141.4\,\Omega} \approx 1.556\,\mathrm{A} \)
\( \displaystyle \cos\phi = \frac{R}{Z} = \frac{100}{141.4} \approx 0.707 \)
\( P = 220\times1.556\times0.707\,\mathrm{W} \approx 242\,\mathrm{W} \)
Shortcut: Since \( R = X_L \), the impedance is \( Z = \sqrt{2}\,R \), so \( I^{2} = V^{2}/(2R^{2}) \) and \( P = I^{2}R = V^{2}/(2R) \).
\( \displaystyle P = \frac{220^{2}}{2\times100}\,\mathrm{W} = 242\,\mathrm{W} \)