How does exactly higher capacitance have more bang for your buck ?

[The_Lobster]

How does exactly higher capacitance have "more bang for your buck"?

Hi!

I'm trying to really grasp the concept of capacitance. Whenever I see a description of the definition, $$C=Q/V$$, they always say either: "More charge stored per potential", or "more bang for your buck".

I don't really see how more charge per potential relates to more energy in the capacitor?

By using $$W = 1/2 * C * V^2$$, we get the same amount of energy if V = 2V and Q = 4C, as if V = 4V and Q = 2C (in the former case C = 2F, and in the latter C = 0.5F).

Could anyone please clarify why having more charge per potential means "more energy is stored"? or how that relates to having "more bang for your buck"?.

Also, keeping in mind that potential is potential energy per unit charge, $$U = qV$$, shouldn't there be more potential energy all together if there is more charge AND more potential?

Sorry if this should be simple stuff! I just feel every definition I've read jumps over exactly *why* more charge per potential means more energy stored...

 

[mrspeedybob]

If C is 1 farad and you charge to 1 volt then you have 1 coulomb of charge. If C is 2 farads and you charge to 1 volt then you have 2 coulombs.

Charge per potential
Coulombs per potential
coulombs per volt
Q per volt
Q per V
Q/V

All identical, I just replaced words wit symbols.