# Conductance and conductivity

## The definition of conductance

The conductance of a component tells you how good a conductor it is. The higher the conductance the better the component is at conducting.

Conductance is just the inverse of resistance. The symbol for conductance is G (heaven knows why) and the unit of conductance is the siemens, S, named after the 19th century German engineer and industrialist Ernst Werner von Siemens. It used to be called the mho, which is just ohm written backwards.

R = V/I so conductance is just the inverse of this: G = I/V.

## Why conductance is a more useful concept than resistance

When we first learn about electricity we tend to talk about conductors and insulators. The idea of conductance fits in quite nicely with this. If something's a good conductor it has a high conductance.

The idea of resistance is often imagined as something external resisting the current somehow. It's much more natural to think of some things just being good conductors, rather than being the victim of this external effect called resistance.

Remember also that batteries are constant voltage providers (if you ignore internal resistance). It's the current drawn from the battery that changes. That depends on what's in the circuit.

Remember that R = V/I (ohms = volts per amp). In other words you're asking 'I wonder what voltage I need for a current of 1 amp to flow through my component?'

This is a bit topsy-turvey because a component, like a bulb or a motor, is normally designed to run at a specific voltage. You don't just go around changing it.

Conductance, G = I/V (siemens = amps per volt). In other words you're asking 'I wonder what current I get when I put 1 volt across this component?'

This makes much more sense because you typically specify the voltage (by for example connecting a component to a particular battery) and measure the current you get.

You also have the link 'high conductance, big current'.

## Conductivity

Conductivity is the inverse of resistivity. It's normally represented by σ (the Greek small letter sigma, presumably to tie it to S, the abbreviation for the siemens). The unit of conductivity is the siemens per metre (see below).

Again it's a material property rather than a component property. So you talk about the conductivity of copper but the conductance of *this* piece of copper wire.

A piece of wire has a high conductance if it's short and fat. So the conductance of a piece of wire depends on

- what it's made from (the conductivity, σ)
- how long it is (the length, l; the longer the wire the lower the conductance)
- its cross-sectional area (area, A; the bigger the area, the higher the conductance)

So G = σA/l. Rearranging we get σ = Gl/A, the units for which are Sm/m^{2}, which is just S/m.