Consider a parallel-plate capacitor. Charge is stored physically on electrodes ("plates") which are flat and parallel to one another. If one electrode has charge +Q and the other electrode has charge -Q, and V is the potential difference between the electrodes, then the capacitance C is C = Q/V. But, now, let's think about the energy stored in the electric field between the electrodes of this parallel-plate capacitor. As stated in Griffiths on page 105, "How much work W does it take to charge the capacitor up to a final amount Q?" It turns out that W is W = 1/2 CV². So, (i) the capacitor's capacitance C goes like 1/V; and (ii) the energy W stored in the electric field goes like V². Are statements (i) and (ii) at odds with one another? I am sure that they cannot be. But conceptually I am having difficulty. We desire high capacitance – we want to put as much charge on the electrodes as possible, because if we accomplish this, then I think that will increase the energy density of the system. But is what I just said true? If we manage to increase Q, then by V = Q/C, the potential difference V between the plates will also increase. This, I think, is why capacitor electrodes are separated by a material (such as a polarizable dielectric material like a slab of plastic); otherwise V will become too large and the breakdown voltage will be reached, generating a spark. But, now, the equation W = 1/2 CV² (where I think that W can be conceptualized as the energy stored in the electric field between the electrodes) seems to say that as V increases, so does the energy W, quadratically. So, my question is, do we want a capacitor to have a large potential difference V or a small potential difference V? If V is large, then W is large (which we want), but C is small (which we do not want). Am I somehow thinking of two different potential differences V and confusing them?