Capacitance doesn't make sense to me, compared to voltage...

[MCAT guy]

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So the equation of capacitance is C = Q/V

This means the more charge I have the higher the capacitance. That makes sense. Capacitance is storing up a charge, which eventually equals the emf of the battery.

So then why in the world is voltage on the bottom of the equation? This would mean I get more and more capacitance by have a lower potential difference? This doesn't make sense to me, I would think that the relationship should be direct. Like if I have an emf that goes to infinity then I should have some amazing capacitance, right? But the equation is saying, as my voltage drops to zero my capacitance gets really high...

This isn't very intuitive to me, what am I missing?

 

[lorenzomicron]

well, first of all, capacitance C is not a variable. It is a material property, so talking about "more capacitance" doesn't make sense in a real world kind of way. so, think of it in this way: Q=V*C.

this make sense, because the higher the voltage you put across the capacitor, the more charge the capacitor is holding.

or V=Q/C, if you have less charge then you cant have as high a voltage.

 

[Rayhaan]

Changing charge or voltage does not change capacitance. Capacitance (think capacity) is the possible max that can be stored on the capacitor. Only physical changes like changing area, distance of plates or using a dielectric material will change capacitance.

 

[MCAT guy]

So I could even think of it like this...

Someone figured out that by setting up two metal plates they could charge them, and there was a direct relationship between V = Q.

Then someone decided to call this capacitance and took capacitance to be the ratio created between Q/V. So C = Q/V. But we can't change C because it is not a variable, so we can only make changes to either Q or V. Which consequently, if I move either up or down the other one will follow suit and move up or down respectively?

 

[Rayhaan]

Sort of, I think you've kind of got what capacitance is. Capacitance is just the ability to store charge, and yes you don't change capacitance just my changing the Q or V. What happens when you change Q or V is it just changes how long it will take to build up to the max capacitance. And yes I believe what you stated is correct, when you manipulate Q or V the other changes accordingly, but the capacitance does not.

Just remember that C is not changed by Q or V, only by physical changes to it like area, distance, or dielectric materials.

A good example is this: if you have 2 circuits that are identical and each has an identical capacitor in it. In one of the circuits put a resistor before the capacitor (so the current has to flow through the resistor before the capacitor).

1) Is the capacitance the same in both? Yes because they are identical capacitors
2) Is the voltage to both the same? No because the resistor causes a voltage drop in the one, but still the capacitance is the same
3) Is the charge (q) the same in both? In this case yes since its a system in series and Q which is basically the current is the same in a series

 

[venacontracta]

Qualitatively:

The goal of a capacitor is to store charge, so a "good capacitor" stores a lot of charge easily. The way you charge a capacitor is by putting an electric potential (voltage) across it. If you have a really good capacitor, it will store a lot of charge even when you put a small voltage across it. If you have a relatively bad capacitor, you'll have to put a larger voltage across it in order to get it to store the same amount of charge.

Quantitatively:

How "good" a capacitor is is described by capacitance, which is the charge stored on the capacitor per unit of electric potential which is put across it (C = Q/V). So, if I can build up a charge of x coulombs on my "good capacitor" by putting 5 volts across it, but my relatively "bad capacitor" requires 10 volts across it to build up the same charge, my good capacitor has double the capacitance of my bad capacitor.