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Fsc 2nd Year chapter No :1 | ELECTROSTATICSFsc 2nd Year chapter No :1 | ELECTROSTATICS
ENERGY STORED IN A CAPACITOR
Energy Stored on a Capacitor
The energy stored on a capacitor can be calculated from the equivalent expressions:
This energy is stored in the electric field.
A capacitor = = x 10^ F which is charged to voltage V= V
will have charge Q = x10^ C
and will have stored energy E = x10^ J.
From the definition of voltage as the energy per unit charge, one might expect that the energy stored on this ideal capacitor would be just QV. That is, all the work done on the charge in moving it from one plate to the other would appear as energy stored. But in fact, the expression above shows that just half of that work appears as energy stored in the capacitor. For a finite resistance, one can show that half of the energy supplied by the battery for the charging of the capacitor is dissipated as heat in the resistor, regardless of the size of the resistor.
Storing Energy in a Capacitor
The energy stored on a capacitor can be expressed in terms of the work done by the battery. Voltage represents energy per unit charge, so the work to move a charge element dq from the negative plate to the positive plate is equal to V dq, where V is the voltage on the capacitor. The voltage V is proportional to the amount of charge which is already on the capacitor.
Element of energy stored: If Q is the amount of charge stored when the whole battery voltage appears across the capacitor, then the stored energy is obtained from the integral:
More detail Calculation This energy expression can be put in three equivalent forms by just permutations based on the definition of capacitance C=Q/V.
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