A series LCR circuit with an inductor, a capacitor and a resistor of resistance 50 \( \Omega \) is connected to an ac source of 24 V, 50 Hz. The impedance of the circuit is 56 \( \Omega \). The average power dissipated in the circuit is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9.18 W
The average power in a series LCR circuit is dissipated only in the resistor, \( P = I_{\mathrm{rms}}^{2}R \), where the rms current is set by the impedance.
\( \displaystyle I = \frac{V}{Z} = \frac{24}{56} = 0.4286\,\mathrm{A} \)
\( \displaystyle P = I^{2}R = (0.4286)^{2}\times50 = 9.18\,\mathrm{W} \)
The same result follows from \( P = VI\cos\phi \) with \( \cos\phi = R/Z = 50/56 \).