A series LCR circuit has inductance L = 10 H, capacitance C = 10 μF and resistance R = 50 Ω. It is connected to V(t) = 200 sin(100πt) volts. Find the resonance frequency f₀ and source frequency f.
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Question

A series LCR circuit has inductance L = 10 H, capacitance C = 10 μF and resistance R = 50 Ω. It is connected to V(t) = 200 sin(100πt) volts. Find the resonance frequency f₀ and source frequency f.

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G1 Physics · Accepted Answer

Step 1: For a series LCR circuit, f₀ = 1/(2π√(LC)). Step 2: Here L = 10 H and C = 10 μF = 10⁻⁵ F; therefore LC = 10⁻⁴ s². Step 3: ω₀ = 1/√(LC) = 100 rad/s, so f₀ = 100/(2π) = 50/π Hz. Step 4: From V(t) = 200 sin(100πt), source angular frequency ω = 100π rad/s. Step 5: f = ω/(2π) = 50 Hz. Final answer: (B) f₀ = 50/π Hz, f = 50 Hz.