(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The question says

A capacitor of capacitance C is given a charge Q . at time t = 0 This capacitor is then connected to another identical capacitor which was initially uncharged through a resistance R .

Find the charge on the second capacitor as a function of time .

( I am assuming that the second capacitor is the uncharged capacitor .)

2. Relevant equations

Charging a capacitor through resistance R and Potential difference ε :

Q(t) = εC(1 -e^(-t/RC) )

where e is the constant ( e = 2.78... )

Discharging a capacitor through a resistance r

Q(t) = Q(initial) * e^(-t/RC)

where e is the constant ( e = 2.78... )

The Answer to the question is :

Q(t) = Q/2(1-e^(-2t/RC))

3. The attempt at a solution

Alright so the Capacitor 1 initially had charge Q so when it will be connected to another uncharged capacitor it will discharge whereas the other capacitor which was initially uncharged will get charged and the total charge will remain constant at any time t.

So if the first capacitor is getting Discharged then

Q(t) = Q(* e^(-t/RC) )

And the second one is getting discharged so

Q(t) = εC(1 -e^(-t/RC) ) -------- (i)

Since the Potential difference ε itself is a function of time so ,

I went to the charge on first capacitor and used

Q = Cε

ε = Q/C

Since C is constant so the ε across first capacitor will also be changing as (and the 1 capcitor is discharging also)

ε(t) = [Q * e^(-t/RC) ]/C

so now I substitute this in (i)

Q(t) = [Q * e^(-t/RC) ]/C * C(1 -e^(-t/RC) )

so the charge at t on the second will be

= [Q * e^(-t/RC) ] * (1 -e^(-t/RC) )

but the answer is

Q(t) = Q/2(1-e^(-2t/RC))

Where am i wrong ?

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# Homework Help: Charging and Discharging capacitor problem .

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