Why is the Energy in Capacitance Formula (CV^2)/2 Instead of QV?

Thread starter semc
Start date Nov 2, 2006
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Capacitance Energy

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SUMMARY

The energy stored in a capacitor is calculated using the formula (CV^2)/2, where C represents capacitance and V represents voltage. This formula arises from integrating voltage with respect to charge, Q, which varies as the capacitor charges. While the voltage from the battery remains constant, the voltage across the capacitor increases from 0 to V as it charges, leading to the conclusion that not all energy from the battery, represented as QV, is stored in the capacitor.

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Understanding of basic electrical concepts, including voltage, charge, and capacitance.
Familiarity with calculus, specifically integration techniques.
Knowledge of energy storage in capacitors and their charging behavior.
Basic principles of circuit theory, particularly in relation to capacitors and batteries.

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Nov 2, 2006

semc

Hi, why is it that when u integrate V wrt to Q u get (CV^2)/2 instead of QV since voltage across is constant?

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Nov 3, 2006

Doc Al

Mentor

The voltage across the capacitor is not constant. The voltage delivered by the battery is constant, so the total energy from the battery is QV, but not all of that energy ends up in the capacitor.