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

In a series LCR circuit, resonance occurs when the inductive reactance equals the capacitive reactance ($X_L = X_C$). The resonant angular frequency is defined as $\omega_0 = 1/\sqrt{LC}$ . The resonant frequency in Hertz is calculated using the formula $
u_0 = \frac{1}{2\pi\sqrt{LC}}$ . Given $L = 10 	ext{ mH} = 10^{-2} 	ext{ H}$ and $C = 1 	ext{ \mu F} = 10^{-6} 	ext{ F}$, we have: $
u_0 = \frac{1}{2\pi\sqrt{10^{-2} 	imes 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-8}}} = \frac{1}{2\pi 	imes 10^{-4}} = \frac{10000}{2\pi} \approx \frac{10000}{6.283} \approx 1591.5 	ext{ Hz}$, which is approximately **1.59 kHz**.

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