A series LCR circuit with inductance $10 ext{ H}$, capacitance $10 ext{ }\mu ext{F}$, resistance $50 ext{

Question

A series LCR circuit with inductance $10	ext{ H}$, capacitance $10	ext{ }\mu	ext{F}$, resistance $50	ext{ }\Omega$ is connected to an ac source of voltage, $V = 200\sin(100\pi t)	ext{ volt}$. If the resonant frequency of the LCR circuit is $f_0$ and the frequency of the ac source is $f$, then

Accepted Answer

Resonant frequency $f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{10 	imes 10 	imes 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-4}}} = \frac{1}{2\pi 	imes 10^{-2}} = \frac{100}{2\pi} = \frac{50}{\pi}	ext{ Hz}$. The source frequency $f$ is derived from $\omega = 100\pi$, so $2\pi f = 100\pi$, which gives $f = 50	ext{ Hz}$.

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