A capacitor of 250,mu F is connected in paral | vedclass

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(C) Given:Capacitance, $C = 250\,\mu F = 250 	imes 10^{-6}\,F$Inductance, $L = 0.16\,mH = 0.16 	imes 10^{-3}\,H$Resistance, $R = 20\,\Omega$The reso

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$8 	imes 10^5\,Hz$

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(C) Given:Capacitance, $C = 250\,\mu F = 250 	imes 10^{-6}\,F$Inductance, $L = 0.16\,mH = 0.16 	imes 10^{-3}\,H$Resistance, $R = 20\,\Omega$The resonant frequency $f$ for an $LC$ circuit is given by the formula:$f = \frac{1}{2\pi \sqrt{LC}}$Substituting the values:$f = \frac{1}{2 	imes 3.14 	imes \sqrt{250 	imes 10^{-6} 	imes 0.16 	imes 10^{-3}}}$$f = \frac{1}{6.28 	imes \sqrt{40 	imes 10^{-9}}}$$f = \frac{1}{6.28 	imes \sqrt{400 	imes 10^{-10}}}$$f = \frac{1}{6.28 	imes 20 	imes 10^{-5}}$$f = \frac{1}{125.6 	imes 10^{-5}} = \frac{10^5}{125.6} \approx 796.17\,Hz$Note: Based on the provided options, the calculation $f = \frac{1}{2\pi \sqrt{LC}}$ yields approximately $796\,Hz$. However, checking the provided answer key $8 	imes 10^5\,Hz$, it appears there may be a unit discrepancy in the problem statement (e.g., if $L$ were in $\mu H$ or $C$ in $pF$). Given the standard formula, the correct resonant frequency is $f \approx 796\,Hz$.

$A$ capacitor of $250\,\mu F$ is connected in parallel to a coil of inductance $0.16\,mH$, while its effective resistance is $20\,\Omega$. Determine the resonant frequency.

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