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Obtain the expression for the energy stored in a capacitor connected across a dc battery. Hence define energy density of the capacitor. |
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Answer» Solution :Let at a particular instant CHARGE on the plate of capacitor be q and its potential difference be `(q)/(C )` . If an ADDITIONAL charge dg is GIVEN to the capacitor plate, work done for it is given by `dW = (q)/(C ).qq` Therefore, whole process of charging from 0 to Q requires a work `W= int_(0)^(Q)(qdq)/(C )=(1)/(C) [(q^(2))/(2)]_(0)^(Q)=(Q^(2))/(2C)` This work done is stored as the electrostatic potential energy U of the charged capacitor. MOREOVER, Q=CV, where V be the potential difference between the plates of capacitor, HENCE `U= (Q^(2))/(2C)= (1)/(2)QV=(1)/(2)CV^(2)` Energy per unit volume of the capacitor is called its energy density u. It can be easily shown that u `=(1)/(2)in_(0)E^(2)` where E = electric field between the plates of capacitor. |
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