An inductor of reactance 100, a capacitor of reactance 50, and a resistor of resistance 50 are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

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Solution

Q.
An inductor of reactance 100 $Ω$ , a capacitor of reactance 50 $Ω$ , and a resistor of resistance 50 $Ω$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

Ans.
(1)

$P = V_{rms} I_{r m s} \cos ϕ$

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

$Z = \sqrt{R^{2} + {(x_{L} - x_{C})}^{2}}$

$Z = 50 \sqrt{2} Ω$

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

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