A resistor of 50 Omega,an inductor of self-in | vedclass

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(B) Given: $L = \frac{3}{\pi^2} \ H$ and $f = 50 \ Hz$.Since the voltage and current are in phase,the circuit is in resonance.At resonance,the inducti

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$0.33 	imes 10^{-4} \ F$

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(B) Given: $L = \frac{3}{\pi^2} \ H$ and $f = 50 \ Hz$.Since the voltage and current are in phase,the circuit is in resonance.At resonance,the inductive reactance equals the capacitive reactance,so $X_C = X_L$.$\frac{1}{\omega C} = \omega L \implies C = \frac{1}{\omega^2 L} = \frac{1}{(2\pi f)^2 L} = \frac{1}{4\pi^2 f^2 L}$.Substituting the values:$C = \frac{1}{4 \pi^2 	imes (50)^2 	imes \frac{3}{\pi^2}} = \frac{1}{4 	imes 2500 	imes 3} = \frac{1}{30000} \ F$.$C = \frac{1}{3} 	imes 10^{-4} \ F \approx 0.33 	imes 10^{-4} \ F$.

$A$ resistor of $50 \Omega$,an inductor of self-inductance $\left(\frac{3}{\pi^2}\right) H$,and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \ V$ and $50 \ Hz$. When the voltage and current are in phase,the value of capacitance is (nearly):

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