In the given circuit,the voltmeter reads 75 | vedclass

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(D) The circuit is a series $LCR$ circuit connected to an $AC$ source of $75 \ V$ and $500 \ Hz$.The voltmeter is connected across the resistor $R$,an

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$10$

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(D) The circuit is a series $LCR$ circuit connected to an $AC$ source of $75 \ V$ and $500 \ Hz$.The voltmeter is connected across the resistor $R$,and it reads $75 \ V$. Since the source voltage is also $75 \ V$,the voltage across the resistor is equal to the source voltage $(V_R = V_{source} = 75 \ V)$.This implies that the voltage across the combination of inductor and capacitor must be zero $(V_L - V_C = 0)$,which occurs at resonance.At resonance,the inductive reactance equals the capacitive reactance: $X_L = X_C$.The resonant frequency is given by $f = \frac{1}{2 \pi \sqrt{LC}}$.Given $f = 500 \ Hz$ and $L = 10 \ mH = 10 	imes 10^{-3} \ H = 10^{-2} \ H$.Substituting the values: $500 = \frac{1}{2 \pi \sqrt{10^{-2} 	imes C}}$.Squaring both sides: $250000 = \frac{1}{4 \pi^2 	imes 10^{-2} 	imes C}$.Using $\pi^2 = 10$: $250000 = \frac{1}{4 	imes 10 	imes 10^{-2} 	imes C} = \frac{1}{0.4 	imes C}$.$C = \frac{1}{250000 	imes 0.4} = \frac{1}{100000} = 10^{-5} \ F$.Converting to $\mu F$: $C = 10^{-5} 	imes 10^6 \ \mu F = 10 \ \mu F$.

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

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