Concept of Capacitance

Concept of Capacitance

• Consider two conducting materials M1 and M2 which are placed in a dielectric medium having permittivity Ɛ. The material M1 carries a positive charge Q while the material M2 carries a negative charge, equal in magnitude as Q. There are no other charges present and total charge of the system is zero. In conductors, charge cannot reside within the conductor and it resides only on the surface. Thus for Mi and M2, charges + Q and - Q reside on the surfaces of M- and M2 respectively. This is shown in the Fig. 5.10.1.

 • Such a system which has two conducting surfaces carrying equal and opposite charges, separated by a dielectric is called capacitive system giving rise to a capacitance.

• The property of a capacitor to store an electrical energy in the form of static charges is called its capacitance.

• The electric field is normal to the conductor surface and the electric flux is directed from M- towards M2 in such a system. There exists a potential difference between the two surfaces of M- and M2. Let this potential is V^. The ratio of the magnitudes of the total charge on any one of the two conductors and potential difference between the conductors is called the capacitance of the two conductor system denoted as C.

C = Q / V₁₂

In general, C = Q / V

where          Q = Charge in coulombs

V = Potential difference in volts

The capacitance is measured in farads (F) and

1 farad = 1 Coulomb / 1 volt

• As charge Q resides only on the surface of the conductor, it can be obtained from the Gauss's law as,

• While V is the work done in moving unit positive charge from negative to the positive surface and can be obtained as,

Hence capacitance can be expressed as,

• If the charge Q is increased, then  get increased by same factor. The voltage V also increases by same factor. Thus the ratio Q to V remains constant as C. Hence capacitance is not the function of charge, field intensity, flux density and potential difference.

Key Point : The capacitance depends on the physical dimensions of the system and the properties of the dielectric such as permittivity of the dielectric.

Review Question

1. Explain the capacitance and derive its basic expression.

2. Define capacitance.