Question

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 $25kHz$. The value of k is:

• A. $3.0$
• B. $2.1$
• C. $1.56$
• D. $1.7$

Answer 1

The correct option is C $1.56$

Natural frequency $=125000Hz$

New frequency $=125000-25000$

$=100000Hz$

Frequency of L-C circuit

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

So, $2\pi f_1=\frac{1}{\sqrt{L{C}_1}}$ ---(1)

$2\pi f_2=\frac{1}{\sqrt{L{C}_2}}$ ---(2)

Dividing (1) by (2)

$\frac{f_1}{f_2}=\sqrt{\frac{C_2}{C_1}}$

$\sqrt{\frac{C_2}{C_1}}=\frac{125000}{100000}=\frac{5}{4}$

$\frac{C_2}{C_1}=\frac{25}{16}$

$k=\frac{C_2}{C_1}=\frac{25}{16}=1.56$