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In a series LCR circuit having \(L = 8.0\) H, \(C = 0.5\,\mu\text{F}\), and \(R = 100\,\Omega\), the resonance frequency in rad/s is

1. 600 rad/s
2. 600 Hz
3. 500 rad/s
4. 500 Hz

Correct answer: 500 rad/s

Solution

The resonance angular frequency of a series LCR circuit is \(\omega_0 = 1/\sqrt{LC}\). With \(L = 8\) H and \(C = 0.5\,\mu\text{F} = 0.5\times10^{-6}\) F, \(LC = 4\times10^{-6}\), so \(\omega_0 = 1/\sqrt{4\times10^{-6}} = 500\) rad/s.

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