# Dimensions and materials of a capacitor

• August 4th 2007, 10:23 AM
Dean
Dimensions and materials of a capacitor
The below question is coming up in a exam of mine soon, does anyone have the answer?

Q. Describe with the aid of diagrams how the dimensions and materials of a capacitor influence its operation.
• August 4th 2007, 10:38 AM
topsquark
Quote:

Originally Posted by Dean
The below question is coming up in a exam of mine soon, does anyone have the answer?

Q. Describe with the aid of diagrams how the dimensions and materials of a capacitor influence its operation.

There's no diagram for what the material does (unless you want to get into how the electron shells set up dipoles in the dielectric material...I don't imagine many people want to do that. ;) ) The reaction of a material to an applied electric field is summed up through the dielectric constant, $\varepsilon$. Generally the larger the dielectric constant of the material that is placed between the capacitor plates, the more charge (and hence energy) the capacitor can store.

As far as the dimensions of the capacitor is concerned if you look at the derivation of the capacitance for several types of capacitors (such as parallel plate, spherical, and cylindrical) you will see that there is an inverse relationship between the capacitance and the distance between the plates:
$C \propto \frac{1}{d}$
(I think the capacitance is actually inversely proportional to ln(d) for the spherical capacitor. I'd have to look that one up to be sure.)

Likewise the area of the capacitor plates (as you might expect) is directly proportional to the capacitance.
$C \propto A$

I'd advise learning at least one derivation of the capacitance to show for answering the question to provide an example of these statements.

Here's a bit of trivia that might or might not be useful to you in this: Most capacitors you buy on the market (the long thin ones anyway) are actually parallel plate capacitors that have been rolled into a cylindrical shape. I imagine the reason is that they are easier to build than a cylindrical capacitor, but there may be other reasons. It might be fruitful to look into this. (Or perhaps not.)

-Dan