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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 the equation for variation of charge on capacitor and current in the inductor with time taking at the instant at which inductor is connected to the capacitor at t = 0

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Given `q_m = CV_m = 30 mu C`
at `t = 0 , q = 0`
`rArr q _((t)) = q _m cos omegat " where " omega = 1/(LC)`
`:. Omega = 1/sqrt(1.5 xx 10^(-6) xx 15 xx 10^(-3)) = 1/(15 xx 10^(-6))` rad/s
Also,` l = l_m sin omega t[ :.t = (-dq)/(dt)]`
`l_m = q_m xx omega = (30 xx 10^(-6))/(15 xx 10^(-5)) = 0.2 A`
`l = (0.2 A ) sin omega t`
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