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Derive an expression for the energy stored in a parallel plate capacitor of capacitance c when charged up to voltage v. How is this energy stored in the capacitor?

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• The energy stored on a capacitor is based on the work done by the battery in the circuit. 

• The battery voltage represents the energy per unit charge. 

• Hence, the work done to move a charge element dq from the negative plate to the positive plate is equal to V dq. 

• The voltage is proportional to the amount of charge which is already present in the capacitor. 

• Energy stored due to dq = dU = Vdq = q/C dq 

• If q is the amount of charge stored when the battery voltage appears across the capacitor, then by integrating the expression, we can get the stored energy. 

• U = ∫ dU = ∫ q/C dq integrated between 0 and 

• Q = 1/2 Q2/ c = 1/2QV = 1/2 CV2 

Energy Stored in a Capacitor. 

• A capacitor is a device for storing energy. When we connect a battery across the two plates of a capacitor, it gets charged. 

• The work done to charge the capacitor is thus stored in the form of electric potential energy inside the capacitor.

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