Answer :

Energy stored in a capacitor:


The energy stored in a capacitor with capacitance C , charge is given by:



where V is the potential difference across the capacitor.


Power supplied by the battery:


If a battery of emf ϵ gives a current I, then the power supplied by the battery is given by:



Kirchhoff’s loop rule:


The sum of potential differences around a closed loop is zero.


Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:




(a)


By Kirchhoff’s loop rule,



As ϵ is constant,


At t = 0, there is no charge on the capacitor. Hence . So, Vr is maximum at t = 0.



(b) Initially, current flows through the circuit treating capacitor as short-circuit. But as charge accumulates on the capacitor the current reduces with time. It is maximum at t =0.


Using Kirchhoff’s loop rule,




I is max at t = 0 and




(c)


Using Kirchhoff’s loop rule,




As R and ϵ are constant



Current is minimum at equilibrium when capacitor acts as an open switch and current is zero. Hence,



(d)


The energy stored by the capacitor is given by:



As C is constant,



We know from (c) that the maximum potential difference across the capacitor is ϵ. Hence,



(e)


Power delivered by the battery is given by:



As ϵ is a constant,



Using the result from (b), we get




(f)


The resistor converts energy into heat:



As R is constant,



Now, using the result from (b),



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