1.

A 50 μF capacitor, when connected in series with a coil having a resistance of 40Ω, resonates at 1000 Hz. The inductance of the coil for the resonant circuit is ____________(a) 2.5 mH(b) 1.2 mH(c) 0.5 mH(d) 0.1 mHThe question was asked in an international level competition.This key question is from Problems of Series Resonance Involving Quality Factor in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer»

Correct choice is (c) 0.5 mH

To explain: At RESONANCE, XL = XC

Or, 2πfL = \(\FRAC{1}{2πfC} \)

L = \(\frac{1}{4π^2 f^2 C} \)

= \(\frac{1}{4π^2 × (1000)^2 × 50 × 10^{-6}} \)

= \(\frac{1}{39.46×50} \)

= 0.0005

So, L = 0.5 mH.



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