Question

What capacitor in series with a 100 Ω resistor and a 30 mH inductor will give a resonance frequency of 970 Hz ?

Answer 1

Resonance frequency for an LCR circuit is given by:

$f = \frac{1}{2\pi \sqrt{LC}}$

=> $970 = \frac{1}{2\pi \sqrt{0.03C}}$

=> $\sqrt{0.03C} = \frac{1}{2\pi (970)}$

=> $0.03C = [\frac{1}{2\pi (970)}]^2$

=> C = 0.8974 x 10^-6 F = 897.4 nF.

this is the capacitance in series which will give out the resonance frequency of 970 Hz.