Question

A circuit with a resistor, inductor and capacitor in series is resonant with frequency f Hz. If all the component values are now doubled, then the new resonant frequency will be?

(a) 2 f

(b) f

(c) \(\frac{f}{4}\)

(d) \(\frac{f}{2}\)

I got this question during a job interview.

My query is from Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct answer is (d) \(\frac{f}{2}\)

The best I can explain: Resonance frequency = \(\frac{1}{2π\sqrt{LC}} = \frac{1}{2π2\sqrt{LC}}\)

Hence, \(\frac{f}{f_o}  = \frac{\frac{1}{2π\sqrt{LC}}}{\frac{1}{2π2\sqrt{LC}}}\) = 2

∴ f = 2fo.