Q. 695.0( 2 Votes )

A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs

(a) between current and time for the first 10 minutes and

(b) between charge and time for the same period.

Answer :

Charging a capacitor:


A capacitor of capacitance C is being charged using a battery of emf ϵ through a resistance R . A switch S is also connected in series with the capacitor. The switch is initially open. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:



Where I0 is the initial current.


The charge is given by:



Note that is known as time constant.


Given,


Resistance of the resistor,


Capacitance,


Emf of the battery,


Now, time constant ,


(a)


The current is given by:



At t =0, we have y-intercept I0.


Now,





Hence, we need to plot



At t = 10min = 600s,




(b)


Now,



Note that the current is in Ampere and time in seconds. The graph will represent exponential decay.


We need to plot



Note that t is in seconds and Q in coulombs.


At t = 10 min = 600s,



The charge will keep on increasing and will almost touch the asymptope at Q = 0.0024C.



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