Conductance: What is it? (Definition, Units & Formula)

Contents

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Key learnings:

Conductance Definition: Conductance is defined as the capacity of a substance to allow the passage of an electrical current, which is the opposite of resistance.
Measurement Units: The unit of measure for conductance is Siemens, symbolized as ‘S’, which helps quantify how easily electricity flows through a material.
Formula for Conductance: Conductance is determined by taking the reciprocal of resistance. This explains that conductance increases as resistance decreases, highlighting how easily electric current can flow through a material.
Conductance vs. Conductivity: While conductance measures how much current flows through a material, conductivity quantifies how a material reacts to electrical fields.
Practical Applications: Understanding conductance is crucial in fields like agriculture for soil health assessment and in water treatment to maintain aquatic life.

What is Conductance?

Conductance, or electrical conductance, describes how readily a specified component carries electricity. It is the ratio of current through the component to voltage across it. For a linear DC element, it is the reciprocal of resistance: G = 1/R.

Resistance describes the voltage needed per unit of electrical current. Between two terminals, it is the ratio of the voltage across the terminals to the current through the component, provided the operating point and conditions are stated.

Resistance is measured in ohms (Ω). Conductance is the current-to-voltage ratio and is measured in siemens (S), where 1 S equals 1 A/V and 1/Ω.

Conductance Formula and Measuring Units

For a linear resistive component, conductance quantifies current per unit applied voltage. It is represented by G and is the reciprocal of resistance R. Ohm’s law, $v=iR$ , gives:

(1) $\begin{align*} R= \frac{v}{i} \end{align*}$

Taking the reciprocal gives conductance, not conductivity. Conductance is the current-to-voltage ratio for the complete component:

(2) $\begin{align*} G= \frac{i}{v} \end{align*}$

The SI unit is the siemens, symbol S. The former name “mho” was the word ohm reversed. For a finite, non-zero DC resistance, conductance is:

(3) $\begin{align*} G= \frac{1}{R} \end{align*}$

How to calculate Conductance?

Conductance can be calculated from resistance, from current and voltage or from a material’s conductivity and the conductor geometry. Only the inputs for the selected method are required.

For a circuit element with resistance $1.25\times 10^{3}ohms$ , use

(4) $\begin{align*} G= \frac{1}{R} \end{align*}$

The protected legacy result $0.8\times 10^{3} Siemens$ has the wrong exponent sign. The correct result is 0.8 × 10⁻³ S, or 0.8 mS, because 1/1,250 = 0.0008.

For an electric circuit that draws 0.3 A at 5 V, Ohm’s law gives

(5) $\begin{align*} R= \frac{v}{i} \end{align*}$

Conductance is reciprocal resistance:

(6) $\begin{align*} G= \frac{1}{R} \end{align*}$

and

(7) $\begin{align*} G= \frac{i}{v} \end{align*}$

Substitution gives G = 0.06 S.

Conductance can also be calculated for a uniform wire with radius r, length L and known material resistivity or conductivity. For conductivity $\sigma$ that is uniform and independent of field, the relationship is:

(8) $\begin{align*} \frac{G= (Area\times\sigma)}{L} \end{align*}$

where $Area=\pi r^{2}$

For an iron rod with radius 0.001 m, length 0.1 m and assumed $\sigma$ of $1.03\times10^{7}$ S/m, $Area=\pi r^{2}$ gives $3.14\times 10^{-6}$ m². Substitution gives about 324 S. Actual conductivity varies with alloy, purity and temperature.

Conductivity

Electrical conductivity is a material property that relates current density, and therefore transport of electrical energy, to an applied electric field. Conductance is a property of a particular component and also depends on its length, cross-sectional area, temperature and contacts.

Electrical conductivity is expressed as $\sigma$ and measured in siemens per metre (S/m). Its reciprocal is resistivity, not resistance. The reciprocal of resistance is conductance. Thermal conductivity and ionic conductivity describe different transport processes and must not be treated as interchangeable electrical quantities.

Conductivity vs Conductance

Electrical conductivity is the ratio of current density to electric-field strength for an isotropic linear material. It is an intrinsic material property under stated conditions and has units of S/m.

Conductance applies to a defined component or path. Measured in siemens, it is the current-to-voltage ratio for the stated operating condition and depends on geometry, material properties, temperature and contacts.

Applications of Electrical Conductivity Measurement

Electrical Conductivity and Agriculture

Soil electrical conductivity is used mainly as an indicator of soluble salts and salinity. It can correlate with ions including nitrates, calcium and potassium, but it does not identify or measure each nutrient separately.

Soil EC also changes with moisture, temperature, texture, porosity and clay mineralogy. Apparent-EC sensors can map spatial variation, but nutrient decisions require calibrated soil tests and local agronomic interpretation.

Electrical Conductivity and Water Treatment

Water conductivity depends on the types and concentrations of dissolved ions and on temperature. Treatment plants use it to monitor changes in ionic content, salinity or dissolved-solids estimates. Discharge limits and ecological effects depend on the receiving water and the applicable permit; EC alone does not identify individual contaminants.

Electrical Conductivity and Electroplating Bath

Electroplating operations in aerospace, automotive and jewellery production use rinse baths to remove residual process solution from plated parts. Counter-current rinsing can reduce fresh-water use and wastewater volume.

Conductivity measurements can help control rinse-water replacement by indicating ionic carryover. Conversions from conductivity to total dissolved solids or salinity are estimates that depend on solution composition and temperature, so the conversion factor must be validated for the process.