Question

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

​​​​​​​$[$1 Mark$]$

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

Answer 1

The correct option is A $1.1\times {10}^3\text{rad/s}$

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

Thus, angular frequency is given by
$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{27\times {10}^{-3}\times 30\times {10}^{-6}}}=\frac{{10}^4}{9}=1.1\times {10}^3\text{rad/s}$