Definition of capacitance

In many college physics courses, the discussion of capacitance often stays at the level of describing circuit elements. The idea of capacitance is restricted to describing what happens with certain types of electrical devices that can store energy in the electric field between a pair of closely spaced plates.

However, in this review course, I want to encourage you to develop a more general sense of capacitance. The unit of capacitance is the farad, which is a a coulomb per volt. What does it mean, for there to be a relationship between the amount of charge and the potential function.

What capacitance describes is the relationship between the geometry of a charge density and its voltage. When you ask what the arrangement of charge does to its voltage, you are discussing the idea of capacitance. Think about it. A compressed small sphere of like charge has a higher voltage than a larger sphere with the same amount of like charge which has more room to spread out. It would take energy to push the charge on that larger sphere into the smaller one. In other words, the larger sphere has a higher capacitance because it can hold the same charge at a lower voltage.

This general, conceptual sense of capacitance is a useful framework to bring to chemistry. That is why we are going through this discussion, to give you something to chew on for chemistry, even though the nomenclature is not generally used in chemistry. In chemistry, you are often asked to interpret how changes in a charge distribution affect the energy. When like charge is permitted to spread out over greater volume, the voltage of the charge distribution decreases. It has lower energy. Chemistries that let charge spread out, such as resonance delocalization, decrease internal energy.