Question

Resonance frequency of LCR series a.c. circuit is $f_0$. Now the capacitance is made 4 times, then the new resonance frequency will will become

• A. $f_0/4$
• B. $2f_0$
• C. $f_0$
• D. $f_0/2$

Answer 1

Answer: (D)

In LCR series circuit, resonance frequency f₀ is given by
$L\frac{1}{C}{}^2=\frac{1}{LC}$
$=\sqrt{\frac{1}{LC}}=2f_0$
$f_0\frac{1}{2\sqrt{LC}}$ or $f_0\frac{1}{\sqrt{C}}$
When the capacitance of the circuit is made 4 times, its resonant frequency become $f_0^{{}^{\prime }}$
$\frac{f_0^{{}^{\prime }}}{f_0}=\frac{\sqrt{C}}{\sqrt{4C}}$ or $f_0^{{}^{\prime }}=\frac{f_0}{2}$