CAPACITANCE! C = Q/ΔV and so C = ε₀ A/d.

Putting capacitors in parallel increases the effective area while leaving the potential difference unaffected, so the total capacitance increases.

Putting capacitors in series increases the effective potential difference while leaving the charge separation and area unaffected, so the total capacitance decreases.

What do you do if you have a complex arrangement of several capacitors? In the case shown, get C23, then C234, finally C12345. Here is a solved example of a capacitor network.

If we put an insulator between the plates of a capacitor, it polarizes in such a way as to reduce the electric field and potential difference between the plates. If the reduction is by a factor 1/κ, then since C = Q/(ΔV), and 1/(1/κ) = κ, the capacitance is increased by a factor of κ, which is called the dielectric constant.

Putting between the capacitor plates a solid substance which has a much higher breakdown voltage than air not only makes it possible to increase the capacitance by a large amount, but at the same time  provides a mechanical barrier keeping the plates from bending and coming closer as more charge is put on them. Worked example: capacitor with a dielectric.



Many materials will sustain a much stronger electric field without electrons being pulled out of atoms, as compared with air, so putting such "dielectric" materials between capacitor plates can increase the capacitance by 10 to 100 times!

The first capacitor, circa 1745.

Energy Stored in a Capacitor!

SmartPhones use capacitance for touch screens!

In physics,we frequently talk about “grounding” a conductor or a conducting path. What does that mean? It basically means creating a conducting path between a given conductor and the surface of the earth. The idea is that the surface of the earth is practically infinite in area compared to any conductor we are dealing with, and also by comparison is a potential reservoir of charge of basically infinite capacity. So we take the surface of the earth to have a potential of zero. Thus, if we ground a conductor, we bring its potential to zero.

From left to right, the standard symbols for a capacitor, a battery and a ground.  DO NOT confuse them.

Capacitor Networks!
 
Solved Capacitor Problems
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