Conductance

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Conductance (German: Leitwert, also Konduktanz) describes how well a component or conductor conducts electric current. It is the reciprocal of electrical resistance and relates voltage and current via Ohm’s law.

1 Quantity symbol and unit

Conductance has the quantity symbol $G$.
Its unit is the siemens with the unit symbol $\mathrm{S}$.

$$[G]=\mathrm{S}=\frac{1}{\Omega }=\frac{\mathrm{A}}{\mathrm{V}}$$

Relationship to resistance:

$$G=\frac{1}{R}=R^{-1}\text{or}R=\frac{1}{G}=G^{-1}$$

2 Practical and worked examples

2.1 Conductance of a conductor from geometry and material

$G=\sigma \cdot \frac{A}{l}=\frac{1}{\rho }\cdot \frac{A}{l}$
Example (copper): $A=1.5\mathrm{m}{\mathrm{m}}^2$, effective length $l=40\mathrm{m}$, $\rho =0.0172\frac{\Omega \mathrm{m}{\mathrm{m}}^2}{\mathrm{m}}$
$R=\rho \cdot \frac{l}{A}=0.0172\cdot \frac{40}{1.5}\mathrm{\Omega }\approx 0.459\mathrm{\Omega }$
$G=\frac{1}{R}\approx \underline{2.18\mathrm{S}}$

2.2 Parallel connection of resistors

The total conductance $G_{\Sigma }$ of $n$ resistors connected in parallel can be calculated by adding their individual conductances $G_i$:

$$G_{\Sigma }=G_1+G_2+\cdots +G_n$$

Example: $R_1=100\mathrm{\Omega }\Rightarrow G_1=0.010\mathrm{S}$, $R_2=220\mathrm{\Omega }\Rightarrow G_2=0.004545\mathrm{S}$

$$G_{\Sigma }=0.014545\mathrm{S}\Rightarrow R_{\mathrm{eq}}=\frac{1}{G_{\Sigma }}\approx \underline{68.8\mathrm{\Omega }}$$

2.3 Input conductance of an electric circuit

$$R_{\mathrm{in}}=10\mathrm{k}\Omega \Rightarrow G_{\mathrm{in}}=0.1\mathrm{mS}$$

2.4 Power expressed via $G$

$$P=U\cdot I=G\cdot U^2=\frac{I^2}{G}$$

Example: $U=12\mathrm{V}$, $R=6\mathrm{\Omega }\Rightarrow G=\frac{1}{6}\mathrm{S}$

$$P=G{U}^2=\frac{1}{6}\cdot 144\approx \underline{24\mathrm{W}}$$

3 Typical orders of magnitude

• $R=1\mathrm{\Omega }\Rightarrow G=1\mathrm{S}$
• $R=100\mathrm{\Omega }\Rightarrow G=10\mathrm{mS}$
• $R=10\mathrm{k}\Omega \Rightarrow G=0.1\mathrm{mS}$
• $R=1\mathrm{M}\Omega \Rightarrow G=1\mu \mathrm{S}$
• $R=1\mathrm{G}\Omega \Rightarrow G=1\mathrm{nS}$

4 Example phrasings

• ‘The conductance of the supply cable is $G\approx 2.2\mathrm{S}$.’
• ‘The parallel connection gives $G_{\Sigma }=G_1+G_2$ and thus $R_{\mathrm{eq}}=\frac{1}{G_{\Sigma }}$.’
• ‘The input has a conductance of $0.1\mathrm{mS}$ (equivalent to $10\mathrm{k}\Omega$).’

5 Related quantities and relationships

5.1 Ohm’s law

$$U=R\cdot II=G\cdot UG=\frac{1}{R}$$

5.2 Conductivity and resistivity

$$R=\rho \cdot \frac{l}{A}G=\sigma \cdot \frac{A}{l}\sigma =\frac{1}{\rho }$$

6 Related components

• Conductor, electric line, cable
• Resistor
• Multimeter