Q. 82

Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.



Answer :

Concepts/Formulas used:


Kirchhoff’s loop rule:


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


Capacitance:


If two conductors have a potential difference V between the them and have charges Q and -Q respectively on them, then their capacitance is defined as



Capacitors in series:


If capacitors C1, C2, C3 , … are in series, then the equivalent capacitance is given by:



We can replace C1 and C2 by Ceq. As C1 ans C2 are in series,



Let us drop the subscript and call Ceq just C.




Let the potential across the capacitor C be at time t be Vc. Let the charge at time t be q.



Note that as C1 and C2 are in series,



Applying Kirchhoff’s loop rule ,







We know that



Where B is a constant




Let



Substitute q = 0 at t = 0,



Substituting the value of A back,



where


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