THEORY OF ELECTRICAL CAPACITANCE

Electrical capacitance:

When a conductor is given some charge, its electrostatic potential increases. If an additional charge q raises its potential by V, then it is found that

q varies as V or q = CV . Hence C = q / V

Where C is called the capacitance of the conductor. It depends on the shape and size of the conductor but is independent of its material.

Hence capacitance of a conductor is defined as the ratio of electric charge on it to the electrostatic potential due to that charge. If V = 1, then C = q.

Hence the capacitance of a conductor is numerically equal to the charge required to raise its potential by unity.

SI unit : 1 Farad = 1 Coulomb / 1 Volt.

Def: Capacitance of a conductor is said to be 1 Farad, if 1coulomb of charge raises its potential by 1volt.

Capacitor (or Condenser): An arrangement of two metallic conductors, so that when one is connected to earth, the other conductor has the ability to store a large amount of charge on it , is called a capacitor ( or condenser).

– Grouping of Capacitors in Series and Parallel

The reciprocal of the resultant capacitance of the series combination of a number of capacitors is equal to the sum of the reciprocals of their individual capacitance.

The resultant capacitance of the parallel combination of a number of capacitors is equal to the sum of their individual capacitance.

– Energy Stored in a Charged Capacitor

As a source of e.m.f. is connected across a capacitor, work is done to charge it. As the charge on the capacitor increases, the PD across it also increases. Hence more and more work has to be done to deliver the same amount of charge due to progressively increasing PD across its plates.

The work done in charging a capacitor is stored in it in the form of electrical energy.

Energy stored in a series (or Parallel) combination of capacitors is equal to the sum of the energies stored in the individual capacitors.

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