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.

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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