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What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 μF and ω = 1000 s⁻¹?

1. 1 mH
2. Cannot be calculated unless R is known
3. 10 mH
4. 100 mH

Correct answer: 1 mH

Solution

For maximum current in an LCR circuit, resonance occurs, and the condition for resonance is ω² = 1/(LC). Substituting ω = 1000 s⁻¹ and C = 10 μF = 10 × 10⁻⁶ F, we get L = 1/(ω²C) = 1/((1000)² × 10 × 10⁻⁶) = 1 × 10⁻³ H = 1 mH.

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