In an LCR circuit,the capacitance is changed | vedclass

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(C) The resonant frequency $f_r$ of an $LCR$ circuit is given by the formula:$f_r = \frac{1}{2 \pi \sqrt{LC}}$For the resonant frequency to remain unc

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$L/2$

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(C) The resonant frequency $f_r$ of an $LCR$ circuit is given by the formula:$f_r = \frac{1}{2 \pi \sqrt{LC}}$For the resonant frequency to remain unchanged,the product $LC$ must remain constant:$L_1 C_1 = L_2 C_2$Given that $L_1 = L$,$C_1 = C$,and $C_2 = 2C$,we substitute these values into the equation:$L \cdot C = L_2 \cdot (2C)$Solving for $L_2$:$L_2 = \frac{LC}{2C} = \frac{L}{2}$Therefore,the inductance should be changed to $L/2$.

In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

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