physics//electromagnetism//electric circuit//capacitance

2026-10-05

Capacitance is how much electric charge a conductor, or a pair of conductors, can hold for each volt of voltage, and it decides how much energy a capacitor stores, how fast a signal can change on a wire, and how much charge a neuron's membrane must move to change its voltage. It is measured in farads: one farad holds one coulomb per volt, an enormous amount, so real values are in microfarads, nanofarads and picofarads.

The picture is two plates facing each other with an insulator between them. Put charge on one plate and the opposite charge gathers on the other, held there by the field across the gap; the voltage between them rises as charge is added, V=Q/CV = Q / CV=Q/C. Capacitance is pure geometry plus material: bigger plates hold more charge at the same voltage, a thinner gap holds more, and a dielectric in the gap holds more than air,

C=ε Ad,C = \varepsilon \, \frac{A}{d} ,C=εdA,

with AAA the area of the plates, ddd the gap and ε\varepsilonε the permittivity of the material between them.

Capacitance is room for charge per volt.

The same charge squeezed onto less capacitance stands at a higher voltage, which is why a small object is easier to charge to thousands of volts, and why a thin membrane needs a lot of charge to shift its voltage a little.

A single object has capacitance too, against its surroundings. An isolated sphere's grows with its radius, so a person (roughly a hundred picofarads) reaches thousands of volts with a tiny charge on a dry day (static electricity).

Capacitance sets speed. Every node of a circuit must be charged through some resistance before its voltage changes, so the product of the two, the RC time constant, is the delay of a wire, a gate or an axon.

The cell membrane is a capacitor about 5 nanometres thick, around 1 microfarad per square centimetre (membrane capacitance in Lobeworks/17).