Capacitors in series and parallel


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          As we know energy can be stored in the electric field of a capacitor. To know the amount of energy stored within the electric field of a capacitor let us consider a parallel plate capacitor for an instance. Suppose this capacitor is initially uncharged such that the initial potential difference across the plates is zero. Now, the capacitor is connected to a battery and develops a maximum charge Q. If C is the capacitance of the capacitor then the energy stored in the charged capacitor is given by,

Here ΔV is the potential difference across the capacitor.

A dielectric is a non-conducting material such as rubber, glass or waxed paper etc. When a dielectric is inserted in between the two plates of a capacitor the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance increases by a dimensionless constant k, which is called dielectric constant. It is a property of a material and its value varies from one material to the other. Now the capacitance of a capacitor with dielectric will be: C = kC0, C0 = Capacitance of the capacitor without dielectric. For a parallel plate capacitor the capacitance is given by,

where    is the capacitance of the parallel plate capacitor without dielectric, A = plate area, d = distance between the plates. Since the capacitance of the capacitor increases, the energy of the capacitor accordingly increases and the amount of charge stored also increases. Thus, the capacitor with dielectric has:

(i) an increase in capacitance

(ii) an increase in maximum operating voltage

(iii) a possible increase in mechanical support between the plates, which allows the plates to be close together without touching, thereby decreasing d and increasing C.