# What exactly is capacitance?

1. Aug 5, 2009

### wavingerwin

What exactly is capacitance?

"Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential" according to wikipedia.com

However, following
$$C=\frac{Q}{V}$$
i cannot get the fact that the smaller the voltage between a capacitor, the bigger its capacitance is

Thank you

2. Aug 5, 2009

### kanato

A given capacitor has a constant capacitance. The equation Q = CV tells you that the amount of charge stored on the capacitor is its capacitance constant times the voltage.

3. Aug 5, 2009

### Born2bwire

You are assuming that the charge stays constant. If I were to compare two systems that are both storing the same amount of charge, the system that requires the lower voltage to store the charge has greater capacitance. The potential is a measure of the amount of work that you would have to do to move a unit charge to opposite ends of the capacitor given the steady-state charge distribution. So a higher potential would indicate that it is harder to store a given charge since it requires a larger barrier of work to prevent the charges from migrating.

Last edited: Aug 5, 2009
4. Aug 5, 2009

### wavingerwin

Hmm, so in other words, with low voltage (of a cell), it is hard to "charge" the capacitors since the cell has a low potential difference, hence low energy to store the electrons in the negative plate of the capacitor...

5. Aug 5, 2009

### Born2bwire

Whoops, I meant higher potential, should have did a better review of that post.

If we have have a capacitor that is charged, we need to keep a potential across the capacitor's terminals to keep these charges in place. Without this potential, the charges in the capacitor would move around and neutralize the capacitor (well, they already have a net charge of zero is most circumstances but I mean the storage areas of the capacitor will become neutral). So if the ability to store a charge using a potential is the measure of capacitance, then we should expect that if it takes less potential to store the same amount of charge, then the capacitance should be greater.

6. Aug 5, 2009

### dx

Take two conductors A and B that can store charge. Put equal and opposite charges on them of magnitude Q. The potential difference between A and B is given by V = ∫ E ds. Now if you change the charges each by a factor of k, so that the charges on A and B are kQ and - kQ, the potential difference is ∫ kE ds = k∫ E ds, due to the superposition principle. So we see that the potential difference is proportional to the charge Q. The constant of proportionality is called 1/C, so V = Q/C where C is called the capacitance. The value of the capacitance depends on the shapes of the conductors and their relative position.