Capacitance is the ratio of the charge on a capacitor to the potential difference applied across it.
CAPACITANCE
C Q V
C capacitance Q charge V voltage
It is a scalar quantity with an SI unit of farad (F).
A capacitor has a capacitance of 1 farad if placing a charge of 1 coulomb on it raises its potential by 1 volt. 1 F 1 C V1 The farad is a very large unit; the microfarad µF is a more practical unit.
As charge is added to an insulated conductor its potential increases; a greater amount of work needs to be done to add further charge to it. It is found that the potential of the conductor and the charge on it are directly proportional to each other, i.e. QV. It follows that: Q CV, where C is a constant, called the capacitance of the conductor.
r
Analogy:When we add a litre of water to a number of different-sized containers, the level to which the water rises depends on the area of the base of the container.The greatest depth of water occurs in the narrowest container.
Similarly in electricity, giving the same quantity of charge to different objects will result in their reaching different potentials depending on their electrical ‘size’, i.e. their capacitance. The conductor with the largest capacitance will be raised to the smallest potential.The largest capac- itors can hold the greatest amount of charge before their potentials become so large that breakdown occurs, resulting in a spark.
Fig 16.4: The same volume of water in containers of different diameters results in different heights of water
The capacitance of a charged conductor is increased by bringing an oppositely charged conductor or an earthed conductor near it as illustrated in Fig 16.5. The presence of the negatively charged plate reduces the potential of the positively charged conductor—it now requires less work to bring the 1 C charge towards the conductor.
Work must be done in bringing positive charge to a positive plate because like charges repel.
The negative plate attracts the positive, meaning that less work has to be done to bring the positive charge to the positive plate.
If the
second plate is earthed, the positive plate induces a negative charge on it. The effect is the same as it is with the negative plate in (b).
Induced negative charge
Earthed plate
e2
(a)
(b)
(c) Fig 16.5: Illustration of less work being required to add charge to a conductor when its capacitance is increased
