An LCR circuit as shown in the figure is conn | vedclass

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(C) The voltage across the resistor in an $LCR$ series circuit is given by $V_R = I R$. The voltage $V_R$ is maximum when the current $I$ is maximum.I

Vedclass · Accepted Answer

$23$

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(C) The voltage across the resistor in an $LCR$ series circuit is given by $V_R = I R$. The voltage $V_R$ is maximum when the current $I$ is maximum.In an $LCR$ series circuit,the current is maximum at the resonant frequency $f_r$,where the inductive reactance equals the capacitive reactance $(X_L = X_C)$.The resonant frequency is given by $f_r = \frac{1}{2 \pi \sqrt{LC}}$.Given values: $L = 24 \, H$,$C = 2 \, \mu F = 2 	imes 10^{-6} \, F$.Substituting the values:$f_r = \frac{1}{2 	imes 3.14 	imes \sqrt{24 	imes 2 	imes 10^{-6}}}$$f_r = \frac{1}{6.28 	imes \sqrt{48 	imes 10^{-6}}}$$f_r = \frac{1}{6.28 	imes 6.928 	imes 10^{-3}}$$f_r = \frac{1000}{6.28 	imes 6.928} \approx \frac{1000}{43.5} \approx 22.98 \, Hz \approx 23 \, Hz$.

An $LCR$ circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied. The frequency,at which the voltage across the resistor is maximum,is......$Hz$.

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