A series LCR circuit with R=20; Omega, L=1.5; | vedclass

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(D) Given:$R = 20\; \Omega$$L = 1.5\; H$$C = 35\; \mu F = 35 	imes 10^{-6}\; F$$V = 200\; V$At resonance,the frequency of the supply equals the natur

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$2000$

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(D) Given:$R = 20\; \Omega$$L = 1.5\; H$$C = 35\; \mu F = 35 	imes 10^{-6}\; F$$V = 200\; V$At resonance,the frequency of the supply equals the natural frequency of the circuit,which implies $X_L = X_C$.The impedance of the series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Since $X_L = X_C$ at resonance,the impedance becomes $Z = R = 20\; \Omega$.The current in the circuit is $I = \frac{V}{Z} = \frac{200}{20} = 10\; A$.The average power transferred to the circuit is given by $P = I^2 R$.Substituting the values,$P = (10)^2 	imes 20 = 100 	imes 20 = 2000\; W$.

$A$ series $LCR$ circuit with $R=20\; \Omega, L=1.5\; H$ and $C=35\; \mu F$ is connected to a variable-frequency $200\; V$ $ac$ supply. When the frequency of the supply equals the natural frequency of the circuit,what is the average power (in $W$) transferred to the circuit in one complete cycle?

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