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Question

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Asked by rbhatt16 26th June 2018, 6:11 PM
Answered by Expert
Answer:
 
At time t=0, when switch is closed, capacitor plates are shorted and all the current from battery is passing through Capacitor.
Hence there is no current in the resistor connected across A and B. Hence the circuit is an RC circuit that
charging the capacitor C through the resistance R.
 
Initially, charge on the capacitor is given by
 
begin mathsize 12px style Q left parenthesis t right parenthesis space equals space C E space open parentheses space 1 space minus space e to the power of bevelled fraction numerator negative t over denominator R C end fraction end exponent close parentheses end style .....................(1)
using eqn.(1), potential difference across capacitor plates at initial time is written as 
 
begin mathsize 12px style V left parenthesis t right parenthesis space equals space fraction numerator Q left parenthesis t right parenthesis over denominator C end fraction space equals space E space open parentheses 1 space minus space e to the power of bevelled fraction numerator negative t over denominator R C end fraction end exponent close parentheses space..................... left parenthesis 2 right parenthesis end style
After some time, if enough charges are collected across capacitor plates, curent through capacitor is reduced
and current through resistance connected across AB increases.
After sufficiently long time current through capacitor will be nil and current drawn from the battery is decided by the two resistances.
 
At that time Potential difference across capacitor plates is same as potential difference across resistance
connected betenn points A and B . This potential difference is E/2.
 
Hence we write the potential difference across capacitor as     begin mathsize 12px style V left parenthesis t right parenthesis space equals space E over 2 space open parentheses 1 space minus space e to the power of bevelled fraction numerator negative t over denominator R C end fraction end exponent close parentheses space..................... left parenthesis 3 right parenthesis end style

Answered by Expert 27th June 2018, 3:27 PM
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