The natural frequency of an `LC`- circuit is 1,25,000 cycles per second. Then the capacitor `C` is replaced by another capacitor with a dielectric medium of dielectric constant k. In this case, the frequency decreases by 25 kHz. The value of k is

Options

A. 3
B. 2.1
C. 1.56
D. 1.7

Answer

C

Explanation

As natural frequency i.e.
`f=(1)/(2pisqrt(LC))` or `fprop(1)/(sqrt(C))`
When capacitor C is replaced by another capacitor C' of dielectric constant K, then
`C'=KC`
`therefore (f')/(f)=sqrt((C)/(C'))`
`implies (125000-25000)/(125000)=sqrt((C)/(KC)) implies (100)/(125)=(1)/(sqrt(K))`
`implies K=((125)/(100))^(2)=1.56`