**Electrical resistance and conductance** are two related parameters in an electric circuit. **Electrical resistance**, simply called **resistance**, is a measure that provides information about the opposition offered by a material in the flow of current. On the other hand, **electrical conductance,** or simply **conductance** is a measure of ease with which the material allows the electric current to flow through it. In this article, I will explain electrical resistance and conductance, along with their related concepts, such as **resistivity (or specific resistance)**, **conductivity (or specific conductance)**, etc. So, let’s start with the basic definition of resistance.

## What is Resistance?

Electrical resistance is one of the major parameters in an electric circuit. The following sections cover all the important concepts related to electrical resistance.

**Definition of Resistance**

**Resistance** or **electrical resistance** is defined as the measure of opposition that a material offers in the movement of electrons or electric current. In other words, a numerical value that represents the friction in the movement of electrons or electric current is termed as resistance.

It is a common practice to denote the electrical resistance by the letter *R*.

Electrical resistance is also known as **electric friction**. This is because it results in the conversion of the kinetic energy of electrons into heat. In nature, different types of materials offer different amounts of resistance. For example, a conductor offers minimal resistance and allows current to flow very easily, while an inductor offers maximum resistance and disallows electric current to flow through.

Hence, the choice of material for a particular application is made on the basis of its electrical resistance.

**Resistance Formula**

The resistance of a conductor can be measured using different kinds of formulae depending on the known circuit parameters.

The resistance of a given conductor can be determined by using the following empirical formula,

$$R=\frac{ρl}{a}$$

Where,

*ρ*is the**specific resistance**or**resistivity**of the material.*l*is the length of the conductor.*a*is the area of the cross-section of the conductor.

However, this formula can be used only when the physical dimensions and material of the conductor are known.

Apart from this formula, the resistance of a conductor can also be determined using Ohm’s law i.e.,

$$R=\frac{V}{I}$$

Here, *V* is the voltage across the conductor and *I* is the current through the conductor.

This formula can be used only when the physical conductions like temperature, area, length, etc. of the conductor remain constant.

**Unit of Resistance**

The SI unit of resistance is **Ohm** and is denoted by the Greek letter **Omega (****Ω****)**.

However, from the above-given formula of Ohm’s law, the unit of electrical resistance can also be given in terms of units of current and voltage as follows,

$$\text{Unit of } R=\frac{\text{Unit of Voltage (Volts)}}{\text{Unit of Current (Ampere)}}=\frac{\text{Volt(V)}}{\text{Ampere(A)}}$$

**Factors Affecting Resistance**

The resistance of a material or a conductor can change depending on various parameters. The most important factors that affect the electrical resistance of a conductor are given below.

As we know, the resistance of a conductor is given by,

$$R=\frac{ρl}{a}$$

Hence, the factors affecting resistance will be as follows:

- Resistance is directly proportional to the length of the conductor. Hence, a longer conductor offers more resistance and vice-versa.
- Resistance is inversely proportional to the cross-sectional area of resistance. Thus, a thick conductor would have lower resistance and vice-versa.
- Resistance is directly proportional to the nature of the material (specific resistance). Hence, different materials offer different amounts of resistance.
- The resistance of a material also changes with a change in temperature. This change depends on the type of material. For example, the resistance of a conductor increases with an increase in temperature, but the resistance of a semiconductor decreases with an increase in temperature.

Hence, this is all about the electrical resistance of a material. Now, let us discuss the conductance of a material.

## What is Conductance?

Electrical conductance is another key parameter of an electric circuit. All the important concepts related to conductance are explained in the following sections.

**Conductance Definition**

**Conductance** or **electrical conductance** is the measure of ease that a material offers in the movement of electrons or electric current. In other words, the amount of ease in the flow of electric current offered by a substance is known as conductance. It is denoted by the letter ‘*G*’.

**Conductance Formula**

Mathematically, the conductance of a conductor is given as the reciprocal of resistance i.e.,

$$G=\frac{1}{R}$$

Therefore, we can calculate the conductance of a material simply by taking the reciprocal of its resistance.

**Conductance Unit**

As the conductance is nothing but the reciprocal of resistance. Hence, the unit conductance will be **Ohm Inverse (****Ω ^{-1}**

**)**.

The SI unit of conductance is **Mho** and is denoted by the symbol **(℧)**.

However, these days, **Siemen (S)** is used to measure the conductance of a conductor.

Hence, this is all about electrical conductance. Now, let us explore the concepts of specific resistance (resistivity) and specific conductance (conductivity), which are also important to understanding the behavior of an electrical circuit.

## What is Resistivity?

**Resistivity**, also called **specific resistance**, is the property of a material by virtue of which it opposes the movement of electrons or electric current. It depends on the nature of the material.

In other words, resistivity is a fundamental property of a substance specifies that how strongly it will resist electric current or how much resistance it will have.

Hence, a low value of resistivity represents that the given material will offer low resistance and allow easy flow of current. Resistivity is usually denoted by the Greek letter **Rho** **(ρ)**.

**Resistivity Formula**

The resistivity of a conductor can be calculated by using the following formula,

$$ρ=\frac{Ra}{l}$$

Hence, if electrical resistance, area of cross-section, and length of a conductor are known, then we can use the above formula to calculate the specific resistance or resistivity of the conductor.

**Unit of Resistivity**

The unit of resistivity can be derived from its formula as below.

$$\text{Unit of }ρ=\frac{Ω×\text{m}^2}{\text{m}}=Ω\text{ m}$$

Hence, the SI unit of resistivity is the **Ohm-meter**.

## Specific Conductance

**Conductivity**, also called **specific conductance**, is the property of a material by virtue of which it allows the movement of electrons or electric current. Similar to resistivity, it also depends on the nature of the material.

In other words, resistivity is a fundamental property of a material that indicates how easily it can conduct electric current or how much electrical conductance it will have.

Conductance is commonly denoted by the Greek letter **sigma (****σ)**.

**Specific Conductance Formula**

Mathematically, the conductivity of a material is defined as the reciprocal of resistivity i.e.,

$$σ=\frac{1}{ρ}$$

**Unit of Conductivity**

Since the conductivity is the reciprocal of the resistivity of a conductor. Hence, its SI unit will be,

$$\text{Unit of }σ=\frac{1}{Ω\text{ m}}=Ω^{-1}\text{ m}^{-1}=℧\text{ m}^{-1}$$

## Conclusion

Hence, this is all about electrical resistance and conductance. In conclusion, electrical resistance is the measure of opposition in the flow of electric current, while electrical conductivity is the measure of ease in the flow of electric current. There are two more related parameters namely, resistivity and conductivity. In the above sections of this article, I have explained all these concepts in detail.

## Numerical Examples

**Q. 1** – If a 4 m long wire has a cross-sectional area of 3 mm^{2}. If the resistivity of the material of wire is 1.68 x 10^{-8} Ω-m. Then, calculate the electrical resistance, conductance, and conductivity of the wire.

**Solution** – Given data,

$$l=4\text{ m}$$

$$a=3\text{ mm}^2=3×10^{-6}\text{ m}^2$$

$$ρ=1.6×10^{-8}\text{ Ω m}$$

Then, the electrical resistance of the wire is,

$$R=\frac{ρl}{a}=\frac{1.6×10^{-8}×4}{3×10^{-6}}=0.0213\text{ Ω}$$

The conductance of the wire is,

$$G=\frac{1}{R}=\frac{1}{0.0213}=46.95\text{ S}$$

The specific conductance of the wire is,

$$σ=\frac{1}{ρ}=\frac{1}{1.6×10^{-8}}=62.5×10^6 \text{ ℧ m}^{-1}$$

**Q. 2** – If a conductor wire has a resistance of 50 Ω. The length of the wire is 5 m, and the area is 2.5 mm^{2}. What is the resistivity of the wire material?

**Solution** – Given data,

$$R=50\text{ Ω}$$

$$l=5\text{ m}$$

$$a=2.5\text{ mm}^2=2.5×10^{-6}\text{ m}^2$$

Hence, the resistivity of the wire material is,

$$ρ=\frac{Ra}{l}=\frac{50×2.5×10^{-6}}{5}=2.5×10^{-5}\text{ Ω m}$$

If you have any queries related to these concepts, please write in the comment box.