16.3. Capacitance http://www.ck12.org
FIGURE 16.8
A battery charging capacitor.Understanding Capacitance
Imagine a constant-voltage source charging two small conducting plates (a small capacitor) that are placed a distance
dapart. Imagine also the same voltage source charging two large conducting plates (a large capacitor) placed a
distancedapart. Do you think both capacitors will eventually acquire the same charge on their plates? If your
intuition tells you no, you’re right! It is certainly reasonable to assume that larger plates would hold more charge
than smaller plates.
Here’s why: The smaller the area of a plate, the less charge the plate can hold because of the electrostatic repulsion
between like charges. However, a larger number of like charges can be separated by the same distance as a smaller
number of charges, over a greater area. We than can say
C∝A
(Note: With enough charge, the electrostatic repulsion can become so great that “electrical breakdown” or “dis-
charge” occurs. The negative charge crosses the gap between the plates and the potential difference between the
plates goes to zero. The battery must then recharge the plates. In all likelihood, though, the capacitor is ruined.)
Now imagine two capacitors with the same-size plates. The plates of one capacitor are very close together and the
plates of the other capacitor are very far apart. Each capacitor is connected to the same voltage source. Do you think
both capacitors will acquire the same charge on their plates? The answer is once again, no.
Here’s why:
We know that the farther apart the charged particles are from each other, the more weakly they interact (Coulomb’s
law). Fewer charges will therefore be attracted to each plate.
We then can say
C∝
1
dThe capacitanceCis, therefore, directly proportional to the area of the plates and inversely proportional to the
distance between the plates of the capacitor.
C∝
A
d