Question

The resonance frequency of an LC-circuit is 125 KHz. Then the capacitor C is replaced by another capacitor with a dielectric medium of dielectric content K. In this case, the resonance frequency decreases by 25kHz. The value of K is

• A. 3
• B. 2.1
• C. 1.56
• D. 1.7

Answer 1

The correct option is C 1.56

$f=\frac{1}{2\pi }\frac{1}{\sqrt{LC}}\to \left(1\right)$
$f^{\prime }=\frac{1}{2\pi }\frac{1}{\sqrt{LKC}}\to \left(2\right)$
$\frac{\left(1\right)f}{\left(2\right)f^{\prime }}=\sqrt{K}=\frac{125}{100}=\frac{5}{4}$
$K=\frac{25}{16}=1.56$