19: Capacitance
- Page ID
- 165865
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A camera flash charges for a second or two, then releases its stored energy in a thousandth of a second, far faster than any battery could deliver it. A heart defibrillator does the same on a larger scale, storing a couple of hundred joules and then driving them through a patient’s chest in a few milliseconds. The touchscreen on your phone senses your finger because your finger changes how much charge a grid of tiny electrodes can hold. And every bit in your computer’s working memory is roughly a hundred thousand electrons, stored or not stored, on a microscopic conductor.
All of these devices are capacitors: two conductors, close together but not touching, that store separated charge and, with it, electrical energy. This chapter asks how much charge a pair of conductors can hold for a given voltage, where the stored energy actually resides, how filling the gap with an insulator changes things, and how capacitors combine when they are connected together. The answers draw on everything in the last three chapters: the fields of Chapter 16, the Gauss’s-law results of Chapter 17, and the potential of Chapter 18.
Learning Objectives
- Define capacitance, and calculate it for parallel-plate, cylindrical, and spherical capacitors.
- Find the energy stored in a capacitor, and the energy density of an electric field.
- Explain how a dielectric increases capacitance, and apply the dielectric constant and dielectric strength.
- Find the equivalent capacitance of capacitors in parallel and in series, and the charge on and voltage across each.