The resonant frequency of a series LCR circui | vedclass

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(B) At resonance frequency $f_R$, the inductive reactance $X_L$ equals the capacitive reactance $X_C$, so $X_L = X_C = X_0$.When the frequency is doub

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$\frac{1}{4} X_{L_1}$

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(B) At resonance frequency $f_R$, the inductive reactance $X_L$ equals the capacitive reactance $X_C$, so $X_L = X_C = X_0$.When the frequency is doubled to $f' = 2 f_R$, the new inductive reactance is $X_{L_1} = 2 \pi (2 f_R) L = 2 X_L = 2 X_0$.The new capacitive reactance is $X_{C_1} = \frac{1}{2 \pi (2 f_R) C} = \frac{1}{2} X_C = \frac{1}{2} X_0$.From $X_{L_1} = 2 X_0$, we have $X_0 = \frac{X_{L_1}}{2}$.Substituting this into the expression for $X_{C_1}$, we get $X_{C_1} = \frac{1}{2} \left( \frac{X_{L_1}}{2} \right) = \frac{X_{L_1}}{4}$.

The resonant frequency of a series $LCR$ circuit is $f_R$. The circuit is connected to a sinusoidally alternating e.m.f. of frequency $2 f_R$. The inductive reactance becomes $X_{L_1}$ and capacitive reactance becomes $X_{C_1}$ after changing the frequency. $X_{C_1}$ is equal to:

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