Question

A charged 30 $\mu$F capacitor is connected to a 27 mH inductor. The angular frequency of free oscillations of the circuit is

• A. $1.1\times {10}^{3}rad{s}^{-1}$
• B. $2.1\times {10}^{3}rad{s}^{-1}$
• C. $3.1\times {10}^{3}rad{s}^{-1}$
• D. $4.1\times {10}^{3}rad{s}^{-1}$

Answer 1

Answer: (A)

$1.1\times {10}^{3}rad{s}^{-1}$

Here, $C=30\mu F-30\times {10}^{-6}F$
$L=27mH=27\times {10}^{-3}H$

$\therefore \omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{27\times {10}^{-3}\times 30\times {10}^{-6}}}=\frac{1}{\sqrt{81\times {10}^{-8}}}$

=$\frac{{10}^4}{9}=1.1\times {10}^{3}rad{s}^{-1}$