Question

A series RLC circuit consists of a $10\Omega$ resistor in series with $L=20\mu H$ and $C=100\mu F$. The new value of $L$ for which the resonant frequecy is one half of the original value.

• A. $10\mu F$
• B. $40\mu F$
• C. $80\mu F$
• D. $400\mu F$

Answer 1

The correct option is C $80\mu F$

The resonant frequency for a series RLC ircuit is given by
$f_0=\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{20\times 100\times {10}^{-12}}}=3558.81Hz$
Now,
$f_0^{\prime }=\frac{f_0}{2}=1779.4Hz=\frac{1}{2\pi \sqrt{L\times 100\mu F}}$
$3.94\times {10}^{-5}=\sqrt{L\times 100\mu F}$
$L=80\mu H$