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A 1.5 mu f capacitor is charged to 20 V...

A `1.5 mu f` capacitor is charged to 20 V. The charging battery is then disconnected and a 15 mH coil is connected in series with the capacitance so that LC oscillations occur. Write current in the inductor as a function of time

A

`l=(0.2A) sin omega t`

B

`l=(0.3A) sin omega t`

C

`l=(0.5A) sin omega t`

D

None of the Above

Text Solution

Verified by Experts

The correct Answer is:
A
Given `q_(m) = C V_(m) = 30 mu C`
at t = 0 , q = 0
`rArr q_((t))=q_(m). Cos omega t ` where `omega=(1)/(sqrt(LC))`
`:. Omega (1)/(sqrt(1.5xx10^(-6)xx15xx10^(-3))=(1)/(15xx10^(-5))` rad/s
Also, `l=l_(m) sin omega t [ :' l = (-dq))/(dt)]`
`l_(m)=q_(m) xx omega = (30 xx 10^(-6))/(15xx10^(-5))=0.2A`
`l=(0.2A) sin omega t`
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