Question

A radio station set is returned from the 108MHz to 90.5MHZ station using a variable capacitor. By what factor is the capacitance change?

Answer 1

The resonance frequency is given by'

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

From this equation,

$\frac{C_2}{C_1}= (\frac{f_1}{f_2})^2= (\frac{108MHz}{90.5MHZ})^2=1.424$

The factor is the capacitance change is

$\frac{f_2-f_1}{f_2}=1-1.424 =0.424$