Capacitance – When we charge a conductor, some work has to be done during the process of transferring the charge to the conductor. This rises the potential of the conductor. Experiments show that the charge Q on the conductor is directly proportional to its potential V i.e.,
Or Q=CV ………… (15.8)
Where C is a constant whose value depends upon the size of the conductor. It is known as capacitance of the conductor.
In Eq 15.8, if V = 1 volt, then Q = C, i.e., the capacitance of a conductor is equal to the amount of charge which raises the known as farad. It is the capacity of a conductor the potential of which rises by one volt when one coulomb charge is given to it.
Capacitor
Charge cannot be stored on a conductor for a long period of time because the stored charges mutually repel each other due to which they spread on the whole surface of the conductor and also tend to leak out from there. In order to store the charge for long periods, a device is used which is known as capacitor. It consists of two thin metal plates, parallel to each other with a very small distance between them the medium between the two plates is air or a sheet of some insulator. This medium is known as dielectric. A plane parallel plate capacitor is shown in Fig. 15.12.
Fig. 15.12 parallel plate capacitor.
If + Q amount of charge is transferred to its plate A, due to electrostatic induction it would induce –Q charge on its outer plate (fig. 15.13). The lines of force between the plates have been shown.
Fig . 15.13 the presence of charge Q on plate A induces a –Q charge on the inner surface of plate B.
There axists a force of attraction between the charges +Q stored on the plate A and the charge –Q induced on the inner surface of the plate B. due to this force of attraction, the charges are bound with the plate and remain stored for long periods.
Due to presence of the charges on the plate, a potential difference V is created between them which is directly proportional to the charge Q given to the plate A.
Or Q = CV ……………. (15.9)
Here C is constant of proportionality, known as the capacitance of the capacitor.
Do You Know?
Unit of capacitance has been named farad after the name of an English scientist Michael faraday who discovered the law of electromagnetic induction.
Example 15.3:
The capacitance of a parallel plate capacitor is 100 pF. If the potential difference between its plates is 50 bolts, find the quantity of charge on its plates.
Solution:
Potential difference between the plates = V = 50V
Capacitance = C = 100 pF
Do you know?
Farad is a very big unit of capacitance. We generally use the following submultiples.
