Question

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

Answer 1

Given, $L=27mH=27\times {10}^{-3}H$

$C=30\mu F=30\times {10}^{-6}F$

Angular frequency in case of free LC oscillations:

${\omega }_0=\frac{1}{\sqrt{LC}}$

Putting values,
${\omega }_0=\frac{1}{\sqrt{27\times {10}^{-3}\times 30\times {10}^{-6}}}$

${\omega }_0=1.11\times {10}^{3}rad{s}^{-1}$

Final Answer: $1.11\times {10}^{3}rad{s}^{-1}$