(D) Maximum power is dissipated in an $LCR$ circuit at the resonant frequency.Given: Inductance $L = 5 \ mH = 5 \times 10^{-3} \ H$,Capacitance $C = 2

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$ \frac{5}{\pi} \times 10^{3} \ Hz $

(D) Maximum power is dissipated in an $LCR$ circuit at the resonant frequency.Given: Inductance $L = 5 \ mH = 5 \times 10^{-3} \ H$,Capacitance $C = 2 \ \mu F = 2 \times 10^{-6} \ F$.The resonant frequency $f_R$ is given by the formula:$f_R = \frac{1}{2 \pi \sqrt{LC}}$Substituting the values:$f_R = \frac{1}{2 \pi \sqrt{5 \times 10^{-3} \times 2 \times 10^{-6}}}$$f_R = \frac{1}{2 \pi \sqrt{10 \times 10^{-9}}} = \frac{1}{2 \pi \sqrt{10^{-8}}}$$f_R = \frac{1}{2 \pi \times 10^{-4}}$$f_R = \frac{10^4}{2 \pi} = \frac{10 \times 10^3}{2 \pi} = \frac{5 \times 10^3}{\pi} \ Hz$.

Class 12 Physics Alternating Current Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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$A$ series $LCR$ circuit contains inductance $5 \ mH$,capacitance $2 \ \mu F$,and resistance $10 \ \Omega$. If the frequency of the $A.C.$ source is varied,what is the frequency at which maximum power is dissipated?

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A
$ \frac{10^{5}}{\pi} \ Hz $
B
$ \frac{10^{-5}}{\pi} \ Hz $
C
$ \frac{2}{\pi} \times 10^{5} \ Hz $
D
$ \frac{5}{\pi} \times 10^{3} \ Hz $

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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$A$ series $LCR$ circuit contains inductance $5 \ mH$,capacitance $2 \ \mu F$,and resistance $10 \ \Omega$. If the frequency of the $A.C.$ source is varied,what is the frequency at which maximum power is dissipated?

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In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

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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