Electrical Capacitance

CAPACITORS AND CAPACITANCE

A capacitor is a system of two conductors separated by an insulator. The conductors have charges; say Q₁ and Q₂, and potentials V₁ and V₂.

Usually, in practice, the two conductors have charges Q and – Q, with potential difference V = V₁ – V₂ between them.

The conductors may be so charged by connecting them to the two terminals of a battery. Q is called the charge of the capacitor, though this, in fact, is the charge on one of the conductors – the total charge of the capacitor is zero.

The electric field in the region between the conductors is proportional to the charge Q. That is, if the charge on the capacitor is, say doubled, the electric field will also be doubled at every point.

Potential difference V is the work done per unit positive charge in taking a small test charge from the conductor 2 to 1 against the field.

 Consequently, V is also proportional to Q, and the ratio Q/V is a constant C.

The constant C is called the capacitance of the capacitor. C is independent of Q or V, as stated above.

The capacitance C depends only on the geometrical configuration (shape, size, separation) of the system of two conductors.

The SI unit of capacitance is 1 farad (=1 coulomb volt^-1) or 1 F = 1 C V^–1. A capacitor with fixed capacitance is symbolically shown as ---||---.

A capacitor with large capacitance can hold large amount of charge Q at a relatively small V.

High potential difference implies strong electric field around the conductors.

The maximum electric field that a dielectric medium can withstand without break-down (of its insulating property) is called its dielectric strength; for air it is about 3 × 10e6 Vm^–1.