In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω.

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Question

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω. The frequency at which resonance occurs is

Accepted Answer

Correct Answer: D — 1.59 kHzStep-by-step Solution:At resonance: XL = XC → resonance frequency:f₀ = 1/(2π√(LC))L = 10 mH = 10 × 10⁻³ H = 10⁻² HC = 1 μF = 10⁻⁶ FLC = 10⁻² × 10⁻⁶ = 10⁻⁸√(LC) = 10⁻⁴f₀ = 1/(2π × 10⁻⁴) = 10⁴/(2π) = 10000/6.283 ≈ 1591.5 Hz ≈ 1.59 kHzWhy other options are wrong:B (15.9 kHz): Ten times too large.A and C give values in rad/s scale — these would correspond to angular frequency ω = 2πf ≈ 10000 rad/s, not 15.9 or 1.59 rad/s.Key Concepts:Resonance condition in LCR circuit: XL = XC, i.e., ωL = 1/(ωC)Resonance frequency: ω₀ = 1/√(LC) → f₀ = 1/(2π√(LC))At resonance: impedance Z = R (minimum), current is maximum.R does not affect resonance frequency (only the quality factor Q = ω₀L/R).

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω. The frequency at which resonance occurs is

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In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω. The frequency at which resonance occurs is

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