Question:
Derive an expression for the energy stored in a parallel plate capacitor.
Answer:
The energy stored on a capacitor is based on the work done by the battery in the circuit. The battery voltage represent 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 = ½ Q2/ c = ½ QV = ½ CV2
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