# Variation of Energy stored in capacitors with $Q$, $V$ and $C$ [closed]

I have a simple doubt that energy $(U)$ stored between two parallel plates of capacitance $C$, having charge $Q$ and applied potential is $V$ is given by three ways by formulas

● $U= \frac{C×V^2}{2}$

● $U= \frac{Q×V}{2}$

● $U= \frac{Q^2}{2C}$

And yes I know how to prove them. But If I am asked that how does energy stored in such capacitor varies with capacitance $C$? OR how it varies with $Q$?. Then should I say that it is inversely proportional to $C$ or it is directly proportional to $C$? Or it is directly proportional to $Q$ or $Q^2$? And also is it directly proportional to $V$ or is independent of it?

I have asked this question because I have come through a question given below:

The plate seperation in a parallel plate capacitor is $d$ and plate area is $A$. If it is charged to $V$ volt and battery is disconnected then work done in increasing the plate separation to $2d$ will be?

I used $W=U2-U1$ and if my calculations are correct then calculating value of $U$ from $U= \frac{C×V^2}{2}$ and $U= \frac{Q^2}{2C}$ gave me two different answers for $W$.

The energy stored is a function of two independent variables $(Q=CV)$, so if asked about how the energy stored depends on the capacitance you need also to be told or state yourself which of the independent variables is kept constant, either voltage or charge in this case.