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(A) The resonant frequency of an $L-C-R$ circuit is given by the formula:$v_{0} = \frac{1}{2 \pi \sqrt{L C}}$This implies that $v_{0} \propto \frac{1}

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decrease to one-half the original value

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(A) The resonant frequency of an $L-C-R$ circuit is given by the formula:$v_{0} = \frac{1}{2 \pi \sqrt{L C}}$This implies that $v_{0} \propto \frac{1}{\sqrt{L C}}$.If the inductance $L$ is doubled $(L' = 2L)$ and the capacitance $C$ is doubled $(C' = 2C)$,the new resonant frequency $v_{0}'$ will be:$v_{0}' = \frac{1}{2 \pi \sqrt{(2L)(2C)}} = \frac{1}{2 \pi \sqrt{4LC}} = \frac{1}{2 \pi \cdot 2 \sqrt{LC}}$$v_{0}' = \frac{1}{2} \left( \frac{1}{2 \pi \sqrt{LC}} \right) = \frac{1}{2} v_{0}$Therefore,the resonant frequency will decrease to one-half of the original value.

If the inductance and capacitance are both doubled in an $L-C-R$ circuit,the resonant frequency of the circuit will

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