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Capacitor energy

Question: If CV2/2 is the standard energy formula for energy (joules) in a capacitor, why does it always equal only half of the energy of the V x I x t (Voltage x Current x Time)?

Answer:

You must remember that with a capacitor the value of the voltage quoted in the formula is the FINAL voltage when fully charged. During the charging process the voltage builds up from zero.
You know the formula C = Q/V so you can see that as the charge on the plates (Q) increases so does the voltage between them.
Think about a graph of Q against V (because Q = CV and C (the capacitance of a given capacitor) is constant) it will be a straight line.
Since energy (as you say) = VIt = QV the area below this line (charge x voltage) is the energy stored and this is QV.
Using C = QV gives the other versions of the formula ( CV2 and Q2/C).

 
 
 
© Keith Gibbs 2011