An inductor of 0.5 ,mH,a capacitor of 200 ,mu | vedclass

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(B) When the current is in phase with the emf in an $LCR$ series circuit,the circuit is in resonance. The resonant frequency $f$ is given by the formu

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(B) When the current is in phase with the emf in an $LCR$ series circuit,the circuit is in resonance. The resonant frequency $f$ is given by the formula: $f = \frac{1}{2 \pi \sqrt{LC}}$.Given: $L = 0.5 \,mH = 0.5 	imes 10^{-3} \,H$,$C = 200 \,\mu F = 200 	imes 10^{-6} \,F = 2 	imes 10^{-4} \,F$.Substituting the values:$f = \frac{1}{2 \pi \sqrt{0.5 	imes 10^{-3} 	imes 2 	imes 10^{-4}}}$$f = \frac{1}{2 \pi \sqrt{1.0 	imes 10^{-7}}} = \frac{1}{2 \pi \sqrt{10 	imes 10^{-8}}}$$f = \frac{10^4}{2 \pi \sqrt{10}} \approx \frac{10000}{2 	imes 3.14159 	imes 3.162} \approx \frac{10000}{19.87} \approx 503.29 \,Hz$.Rounding to the nearest integer value as per the options,$f \approx 500 \,Hz = 5 	imes 10^{2} \,Hz$.

An inductor of $0.5 \,mH$,a capacitor of $200 \,\mu F$ and a resistor of $2 \,\Omega$ are connected in series with a $220 \,V$ ac source. If the current is in phase with the emf,the frequency of ac source will be ................ $\times 10^{2} \,Hz$

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