Question

A series LCR circuit is connected across a source of alternating emf of changing frequency and resonates at frequency ${\text{f}}_o$. Keeping capacitance constant, if the inductance (L) is increased by $\sqrt{3}$ times and resistance(R) is increased by 1.4 times, the resonant frequency now is:

• A. $3^{1/4}{\text{f}}_0$
• B. $\sqrt{3}{\text{f}}_0$
• C. $(\sqrt{3}-1{)}^{1/4}{\text{f}}_0$
• D. ${\left(\frac{1}{3}\right)}^{1/4}{\text{f}}_0$

Answer 1

Answer: (D)

${\left(\frac{1}{3}\right)}^{1/4}{\text{f}}_0$

Resonant frequency of a series LCR circuit is given by the formula

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

Hence, $f_0=\frac{1}{2\pi \sqrt{LC}}$

In second case, $f^{\prime }=\frac{1}{2\pi \sqrt{L^{\prime }C}}=\frac{1}{2\pi \sqrt{\sqrt{3}LC}}=\frac{1}{3^{\frac{1}{4}}}{f}_0$