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In the circuit shown, a capacitor charge...

In the circuit shown, a capacitor charged to a potential difference `V_(0)` is connected to an uncharged capacitor through a resistor at `t=0`, by closing the switch. Find current in the circuit as function of time.
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Text Solution

Verified by Experts

The correct Answer is:
`(V_(0))/(R)e^(-2t//RC)`.
`(V_(0))/(R) e^(-2t//RC)`
Let, at any moment of time, charge flown be `q` then current `i= (dq)/(dt)`
Applying loop rule in the circuit , `- Delta varphi =0`, we get :
`(dq)/(dt)IR -((CV_(0)-q))/(C)+(q)/(C)=0` or
`(dq)/(CV_(0)-2q)=(1)/(RC)dt`
So, `In(CV_(0)-2q)/(CV_(0))=-2 (t)/(RC) for 0 le t le t`
or, `q = (CV_(0))/(2)(-e^((-2t)/(RC)))`
Hence, `i=(dq)/(dt)=(CV_(0))/(2)(2)/(RC)e^((-2t)/(RC))=(V_(0))/(R) e^(-2t//RC)`.
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