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

[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?

 

[Doc Al]

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.

 

[kyle8921]

The reason for this is because the integral of voltage with respect to charge represents the area under the voltage vs. charge curve, which is equal to the energy stored in the capacitor. This area is calculated by taking the average voltage (V/2) and multiplying it by the total charge (Q), resulting in (CV^2)/2. This is known as the energy stored in a capacitor formula. It may seem counterintuitive that the voltage across the capacitor is constant, but the amount of charge that can be stored on the capacitor increases as the voltage increases, resulting in a non-linear relationship between voltage and charge. Hence, the energy stored in the capacitor is directly proportional to the square of the voltage and not just the voltage itself.