A series LCR circuit driven by 300 , V at a f | vedclass

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(A) For maximum average power in an $LCR$ circuit, the circuit must be in resonance.At resonance, the inductive reactance equals the capacitive reacta

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$4$

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(A) For maximum average power in an $LCR$ circuit, the circuit must be in resonance.At resonance, the inductive reactance equals the capacitive reactance, i.e., $X_{L} = X_{C}$.Given $X_{L} = 250 \pi \, \Omega$ and frequency $f = 50 \, Hz$.The formula for capacitive reactance is $X_{C} = \frac{1}{2 \pi f C}$.Equating the two: $250 \pi = \frac{1}{2 \pi (50) C}$.$250 \pi = \frac{1}{100 \pi C}$.$C = \frac{1}{250 \pi 	imes 100 \pi} = \frac{1}{25000 \pi^{2}}$.Given $\pi^{2} = 10$, we have $C = \frac{1}{25000 	imes 10} = \frac{1}{250000} \, F$.$C = 4 	imes 10^{-6} \, F = 4 \, \mu F$.

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