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Question: An charged 30\(\mu\)F capacitor is connected to a 27mH inductor. The angular frequency of free oscil...

An charged 30μ\muF capacitor is connected to a 27mH inductor. The angular frequency of free oscillations of the circuit is

A

1.1×103rads−11.1 \times 10^{3}rads^{- 1}

B

2.1×103rads12.1 \times 10^{3}rads^{1}

C

3.1×103rads13.1 \times 10^{3}rads^{1}

D

4.1×103rads14.1 \times 10^{3}rads^{1}

Answer

1.1×103rads−11.1 \times 10^{3}rads^{- 1}

Explanation

Solution

: Here, C=30μF=30×10−6FC = 30\mu F = 30 \times 10^{- 6}F

L=27mH=27×10−3HL = 27mH = 27 \times 10^{- 3}H

∴ω=1LC=127×10−3×30×16−6=181×10−8\therefore\omega = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{27 \times 10^{- 3} \times 30 \times 16^{- 6}}} = \frac{1}{\sqrt{81 \times 10^{- 8}}}

=1049=1.1×103rads−1= \frac{10^{4}}{9} = 1.1 \times 10^{3}rads^{- 1}