Calculating Conductance: A Step-by-Step Guide

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.

Conductance from Resistance

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}{1.25times 10^3text{ ohms}}=8times10^2text{ siemens})

Conductance when Current and Voltage Are Known

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.

Conductance from Conductivity

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{Asigma}{L})

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

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

Example:

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.