Question

In a series $LCR$ circuit voltage and the frequency of the main supply are $220V$ and $50Hz$ respectively. On taking out the capacitor from the circuit the current lags behind the voltage by ${30}^o$. On taking out the inductor from the circuit the current leads the voltage by ${30}^o$. The power dissipated in the circuit is,
(Assume $R=200\Omega$)

• A. $305W$
• B. $210W$
• C. zero
• D. $242W$

Answer 1

The correct option is D $242W$

The given circuit shows a characteristic same as the series resonance circuit.
( | Phase angle is same when capacitor is removed | = | Phase angle is same when inductor is removed | )
$\Rightarrow X_L=X_C$

In any series resonance circuit, effect of inductor and capacitor gets nullified and ciruit is pure resistive in nature. Hence,

$P=\frac{V^2}{R}=\frac{{220}^2}{200}=242W$.