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
$L\quad \frac{1}{C}\quad^{2}=\frac{1}{LC}$
$=\sqrt{\frac{1}{LC}}=2\quad f_{0}$
$f_{0}\quad \frac{1}{2\,\,\sqrt{LC}}$ or $f_{0}\quad \frac{1}{\sqrt{C}}$
When the capacitance of the circuit is made 4 times, its resonant frequency become $f_{0}^{'}$
$\frac{f^{'}_{0}}{f_{0}}=\frac{\sqrt{C}}{\sqrt{4C}}$ or $f^{'}_{0}=\frac{f_{0}}{2}$