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Parallel Plate Capacitor Capacitance

Capacitance:Different conductors have different capacities to hold electric charge. The capacity of a conductor to hold charge depends upon the shape, size and surroundings of the conductor. The capacity of a conductor to hold charge is called capacitance. 

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 For an isolated conductor when we increase the charge on the conductor, its potential also gets increased. The charge on the conductor is directly proportional to the potential of the conductor.Q α VQ = CVHere C is proportionality constant called as capacitance. So capacitance isC = Q / VUnit of capacitance is coulomb / volt or farad. 

 Parallel Plate Capacitance:A parallel plate capacitor consists of two conducting metal plates X and Y each of area A separated by distance d. The plates can be of any shape. When the plates are connected to a battery, a charge +q appears on plate X and – q appears on plate Y. On each plate the charge is distributed uniformly. As the distance between the plates is small compared to the area of the plate, the electric field is uniform between the plates. 

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The electric field is non uniform at the outer edge of the plates.When there is no material placed between the plates of the capacitor, air acts as a dielectric between the plates. With air as dielectric, the capacitance of parallel plate capacitor is directly proportional to the area of the plate and inversely proportional to the distance between them.C = εo A / dHere εo is the permittivity of airEffect of dielectric on the capacitance of a parallel capacitorIf a dielectric slab of thickness t with dielectric constant K is introduced between the plates of a capacitor then the capacitance isC = εo A / [(d-t) + (t /K)]If the distance between the plates is completely filled with dielectric then d = t, so the above equation reduces toC = εo A / [0 + (t /K)]= K εo A / d