I understand that capacitance is the ability of a body to store an electrical charge and the formula is $C=\frac{Q}{V}$. What I don't understand, however, is why it is defined as coulomb per volt. Of course, the charge in the numerator makes sense but I don't get why capacitance would measured in relation to voltage. For instance, why don't measure the ability to store something by the volume it takes so why not charge per unit volume. Or, according to the equation $C=\frac{Q}{V}$, why would increasing voltage, while keeping charge constant, have any effect on the ability of a body to store charge. Hope you can provide me with some intuition on this topic.
[Physics] Why is capacitance defined as charge divided by voltage
capacitancechargeelectric-circuitselectricityelectrostatics
Best Answer
You can use a high vertical tube to store water in it (fill it from the bottom by pushing the water in)
How much water can you store? It obviously depends on the pressure you apply to push it in. If you push harder, there will be more water stored.
The tube is characterized not the amount of water, but by how easy it is to store the water. Its "capacity" is the cross section, in this picture. The broader, the more water you store with a given effort.
Now this is a direct analogy. The capacitor is never full (= the tube is very high), you can always store more charge, you just have to push harder.
Indeed, there is an upper rim of the tube, when the water flows out. That's when a spark jumps and partially discharges the capacitor. But this is another story.
A still more correct picture is two tubes in which a pump can create a difference in water level.
The question is: why $Q/V$ and not for example $Q/V^2$?
One answer: experiment shows, that a given capacitor will have a linear dependence of stored charge to applied voltage.
Another answer: The field produced by a charge is linearly proportional to $Q$ (Coulombs Law). And so will be the voltage (it's the integral of the field).
... You see, I can view the system from different perspectives, what the cause-effect direction is. You can say, that a high water column produces a high pressure, or you can say that a high pressure will push the water column high.
You may as well say, that a capacitor stores voltage instead of that it stores charge; both is right. The energy is given by the product, and this is what you really care about.