Energy Stored In a Capacitor - Physics 202 Tuesday...

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Physics 202 Tuesday, February 23, 1999 Announcements: none Lecture notes: Energy Stored In a Capacitor At t=0, we close the switch, than electrons are removed from the top plate (by the battery) to the bottom plate. At an instant just after t=0, the amount of charges on the capacitor plates are q. At this instant, the potential difference across the plate is : V 1 = q/C. o Why is ti not V? Because it is not at Q yet. (Q being the final amount of charge) The work necessary (supplied by the battery) to transfer an increment of charge -dq (from the top plate to the bottom plate) is dW = V 1 dq = q/c dq o This work is is needed to transfer charge dq from the bottom to the top plate. o Therefore, the total amount of work required to charge the capacitor from q=0 to q=Q is W= I(integral) dW = I(Integral from 0 to Q) q/C dq = Q 2 / 2C This work by an external source (the battery) is stored as potential energy in the capacitor o U = W = Q 2 / 2C = (1/2)CV 2 o Q = CV The potential energy stored in the capacitor, after the switch was closed for a long time is, ( in building up the electric field) U = (1/2)CV 2
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