Question

A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, what is the value of the capacitor?

(a) 676 μF

(b) 575 μF

(c) 591 μF

(d) 610 μF

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The above asked question is from Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit topic in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct answer is (a) 676 μF

Explanation: We know that fo = \(\frac{1}{2π\sqrt{LC}}\)

Or, 50 = \(\frac{1}{2π\sqrt{5×10^{-3}×C}}\)

Or, C = \(\frac{1}{4π^2×50^2×15×10^{-3}}\) ≈ 676 μF.