How To Calculate Conductance

In electronics, conductance is a measure of the current produced through a circuit element for a given applied voltage. Usually denoted by the letter G, conductance is the reciprocal of resistance, R. The unit of conductance is the siemens (S). The conductance of a conductor depends on many factors, including its shape, dimensions, and the material's conductivity—usually denoted by the Greek letter σ.

Suppose a particular circuit element has a resistance of 1.25 × 10³ ohms. Because conductance is the reciprocal of resistance, we can write:

\(G=\frac{1}{R}\)

Therefore:

\(G=\frac{1}{1.25\times 10^3\text{ ohms}}=8\times10^2\text{ siemens}\)

Consider this example: A voltage (V) of 5 volts generates a current (I) of 0.30 amps in a particular length of wire. Ohm's law tells us that resistance (R) can be easily determined. According to the law:

\(V=IR\)

So:

\(\frac{1}{R}=\frac{I}{V}\)

In this case, it's 0.30 amps ÷ 5 volts = 0.06 Siemens.

Suppose you have a wire with a round cross-section that has a radius r and length L. If you know the conductivity (σ) of the wire material, you can find the conductance (G) of the wire. The relationship between them is:

\(G=\frac{A\sigma}{L}\)

and since cross-sectional area is πr², this becomes:

\(G=\frac{\pi r^2\sigma}{L}\)

Find the conductance of a round piece of iron with a cross-sectional radius of 0.001 meters and length of 0.1 meters.

Iron has a conductivity of 1.03 × 10⁷ siemens/m, and the cross-sectional area of the wire is 3.14 X 10^-6 m. The conductance of the wire is then 324 siemens.