Capacitance of a conductor
When a charge q is given to an isolated conductor, its potential will change. The change in potential depends on the size and shape of the conductor. The potential of a conductor changes by V, due to the charge q given to the conductor.
q α V or q = CV
i.e. C = q/V
Here C is called as capacitance of the conductor.
The capacitance of a conductor is defined as the ratio of the charge given to the conductor to the potential developed in the conductor.
The unit of capacitance is farad. A conductor has a capacitance of one farad, if a charge of 1 coulomb given to it, rises its potential by 1 volt.
The practical units of capacitance are µF and pF.
Consider an insulated conductor (Plate A) with a positive charge 'q' having potential V (Fig 1.22a). The capacitance of A is C = q/V. When another insulated metal plate B is brought near A, negative charges are induced on the side of B near A. An equal amount of positive charge is induced on the other side of B (Fig 1.22b). The negative charge in B decreases the potential of A. The positive charge in B increases the potential of A. But the negative charge on B is nearer to A than the positive charge on B. So the net effect is that, the potential of A decreases. Thus the capacitance of A is increased.
If the plate B is earthed, positive charges get neutralized (Fig 1.22c). Then the potential of A decreases further. Thus the capacitance of A is considerably increased.
The capacitance depends on the geometry of the conductors and nature of the medium. A capacitor is a device for storing electric charges.
The capacitor is a charge storage device. Work has to be done to store the charges in a capacitor. This work done is stored as electrostatic potential energy in the capacitor.
Let q be the charge and V be the potential difference between the plates of the capacitor. If dq is the additional charge given to the plate, then work done is, dw = Vdq
This work done is stored as electrostatic potential energy (U) in the capacitor.
This energy is recovered if the capacitor is allowed to discharge.
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