Question
A charged 30 µF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillation of the circuit?
✓
Answer
Given :$C=30 uF=30 \times 10^{-6} F$
$L =27 mH =27 \times 10^{-3} H$
$\omega_r=?$
We know that $\quad \omega_r=\frac{1}{\sqrt{ LC }}$
or$\omega_r=\frac{1}{\sqrt{27 \times 10^{-3} \times 30 \times 10^{-6}}}$
$=\frac{1}{\sqrt{81 \times 10^{-8}}}=\frac{1}{9 \times 10^{-4}}$
$\omega_r=\frac{10^4}{9}=1.1 \times 10^3 rad s ^{-1}$
$L =27 mH =27 \times 10^{-3} H$
$\omega_r=?$
We know that $\quad \omega_r=\frac{1}{\sqrt{ LC }}$
or$\omega_r=\frac{1}{\sqrt{27 \times 10^{-3} \times 30 \times 10^{-6}}}$
$=\frac{1}{\sqrt{81 \times 10^{-8}}}=\frac{1}{9 \times 10^{-4}}$
$\omega_r=\frac{10^4}{9}=1.1 \times 10^3 rad s ^{-1}$
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