# Capacitance

Capacitance

If equal quantities of water are poured into vessels of different diameters the water will come up to different levels in each. Similarly, when equal charges are given to conductors of different sizes they will acquire different potentials. This may be
demonstrated by standing two unequal metal cans on the caps of two identical electroscopes (Fig. 33.5 (a)). The cans are given equal charges of Q units from an

electrophorus disc. The charged disc is lowered inside a can until it touches the bottom. In this way the whole of the charge is given up to the can and goes to the outside. It will be noticed that the leaf divergence is greater for the small can, showing that it has acquired a higher potential than the large can. The large can is said to have a larger capacitance.

When the two cans are joined by a wire electricity flows from the small can to the large one until the potentials become equalized (Fig. 33.5 (b». This may be compared with the equalization of water levels in two vessels which are connected through a pipe.
Fig. 33.6 illustrates an experiment to show that the capacitance of a metal plate depends on its surface area. The conductor in this case takes the form of a tinfoil  blind which is supported on an insulating roller.

The blind is connected to an electroscope by means of a wire and is then given a charge. The leaf divergence indicates the potential of the blind. If the blind is now unrolled the leaf divergence, and hence the potential, is seen to decrease. Since the charge has remained unaltered, it follows that, as the area increases, the capacitance of the blind increases. The capacitance of a conductor is defined as the ratio of its charge to its potential.