Question

Explain the meaning of the electrical capacity of a conductor. How capacity of a conductor can be increased?

Hint:

Capacity is the charge per unit potential, C = Q/V. Increase it by enlarging the conductor, adding an earthed neighbour, or introducing a dielectric.

Answer 1

Step 1: Meaning of electrical capacity (capacitance).
When a charge \(Q\) is given to an isolated conductor, its potential rises to \(V\). Experiment shows \(Q\propto V\), so \(Q=CV\). The constant \(C\) is called the electrical capacity (capacitance) of the conductor:
\[C=\frac{Q}{V}\]It is the charge required to raise the conductor's potential by one unit. Its SI unit is the farad (F), where \(1\,\text{F}=1\,\text{C/V}\).
Step 2: Physical interpretation.
A large capacity means the conductor can hold a large charge with only a small rise in potential.
Step 3: How to increase the capacity.
(i) Increase the size (surface area) of the conductor. For a sphere \(C=4\pi\varepsilon_0 R\), so a bigger radius gives more capacity.
(ii) Bring an earthed conductor near it. The induced charges lower the potential for the same charge, raising \(C\) (principle of a capacitor).
(iii) Fill the surrounding space with a dielectric of dielectric constant \(K\); the capacity increases \(K\) times.
\[\boxed{C=\frac{Q}{V};\ \text{increase } C \text{ by larger size, a nearby earthed plate, or a dielectric}}\]