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 C_{1} 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 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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A parallel-plate capacitor has plate area 20 cm^{2}, plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy for the capacitor 8.9 μs after the connections are made.

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

HC Verma - Concepts of Physics Part 2