In a series LCR circuit, the inductance $L$ is 10 mH, capacitance $C$ is 1 $\mu$F and resistance $R$ is 100 $\

Question

In a series LCR circuit, the inductance $L$ is 10 mH, capacitance $C$ is 1 $\mu$F and resistance $R$ is 100 $\Omega$. The frequency at which resonance occurs is

Accepted Answer

Resonant frequency $f = \frac{1}{2\pi\sqrt{LC}}$. Given $L = 10 	imes 10^{-3}$ H, $C = 1 	imes 10^{-6}$ F. $f = \frac{1}{2\pi\sqrt{10^{-2} 	imes 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-8}}} = \frac{10^4}{2\pi} \approx \frac{10000}{6.28} \approx 1592$ Hz = 1.59 kHz.

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