Q. 82

# Consider the situ

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 C_{1}, C2, C3 , … are in series, then the equivalent capacitance is given by:

We can replace C_{1} and C_{2} by C_{eq}. As C_{1} ans C_{2} are in series,

Let us drop the subscript and call C_{eq} just C.

Let the potential across the capacitor C be at time t be V_{c}. Let the charge at time t be q.

Note that as C_{1} and C_{2} 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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