Chapter 24: Capacitance

Capacitor

A capacitor is an electronic component that can store electrical charge and then release it. It is made by separating two conducting plates by an insulator. The charge that is stored by capacitor is due to the potential difference. So we can write:

Q α V

Q = kV

 k is a constant specific to the capacitor, this is called the capacitance and is represented by C.

Energy stored in a Capacitor

The top equation shows us that the charge of a capacitor increases with the potential difference across it. If we plot p.d. against charge we get the first graph.

We can derive an equation to find the energy that a capacitor stores by considering the energy transferred during the shaded section on the second graph.

In this section the charge changes from q to q+Δq when p.d. v is applied,

Using E = VQ

Energy stored is E = v Δq

The total energy is equal to the total of all the little rectangular sections and is given by E = ½ QV.

We can use the top equation to derive two more equation for the energy stored by a capacitor.

E = ½ QV

E = ½ CV2

E = ½ Q2/C

The capacitor stores energy but not charge because the charge on plates are equal and opposite, hence there is no resultant charge and energy is stored because there is a charge separation.

The unit of capacitance is Farad.

Capacitors in Parallel

Capacitors in parallel has same p.d. across each capacitor; total charges equal to the sum of charges.

The total charge is given by:

Q = Q1 + Q2 = C1V + C2V

Since V is a common Factor:

Q = (C1 + C2) V

Comparing this with Q = Ctotal V

CTotal = C1 + C2 + C3 + ………..

Capacitors in Series

Capacitor is series; in this p.d. is divided among capacitors so, each capacitor stores same charge.

V = V1 + V2

Q/CTotal = Q/C1 + Q/C2

1/CTotal = 1/C1 + 1/C2