15.1. Capacitors http://www.ck12.org
GuidanceA capacitor is a device that stores charge. It is typically two very large flat plates wrapped in a cylinder with a
dielectric substance in between the two. The dielectric allows the plates to be at a high voltage (and thus store
more charge) without arcing between them. The capacitance, literally tells you how much charge it can hold. The
capacitance of a capacitor only depends on its geometry. Here some important things to keep in mind in regards to
capacitors:- Qrefers to the amount of positive charge stored on the high voltage side of the capacitor; an equal and opposite
amount,−Q, of negative charge is stored on the low voltage side of the capacitor. - Current can flowintoa capacitor from either side, but current doesn’t flow across the capacitor from one plate
to another. The plates do not touch, and the substance in between is insulating, not conducting. - One side of the capacitor fills up with negative charge, and the other fills up with positive charge. The reason
for the thin, close plates is so that you can use the negative charge on one plate to attract and hold the positive
charge on the other plate. The reason for the plates with large areas is so that you can spread out the charge
on one plate so that its self-repulsion doesn’t stop you from filling it with more charge. - Typical dielectric constantsκare roughly 5.6 for glass and 80 for water. What these “dielectric” substances
do is align their electric polarity with the electric field in a capacitor (much like atoms in a magnetic material)
and, in doing so, reduces the electric field for a given amount of charge. Thereby allowing for more charge to
be stored for a given Voltage. - The electrical circuit symbol for a capacitor is two flat plates, mimicking the geometry of a capacitor, which
typically consists of two flat plates separated by a small distance. The plates are normally wrapped around
several times to form a cylindrical shape.
Example 1You create a simple capacitor by placing two .25m square metal plates .01m apart and then connecting each plate to
one end of a battery. (a) If the battery can create a voltage drop of 12V, how much charge can be stored in the
capacitor. (b) If you immersed the whole system in water, how much more charge could you store on the capacitor?
Solution(a): To solve this problem, we can use the equations give above. First we’ll find the capacitance of the two plates
based on their dimensions. Since there is not dielectric between the plates to start, the dielectric constant is 1.