Electrical Resistance and Resistivity – Definition, Formula, Unit and Measurement

According to the electron theory of matter, we know that all matter (solid, liquid, or gas) is made of tiny particles called molecules. A molecule in turn is made up of atoms. Thus, atoms are the basic building blocks of all matter.

An atom consists of a central part called the nucleus, and a space around the nucleus called the extranucleus. The nucleus of an atom contains two particles namely a proton and neutron, while the extra-nucleus contains electrons that revolve around the nucleus in a certain path called the orbit.

The electrons in the last orbit are called the free electrons because they are quite loosely bound to the nucleus, and therefore can be detached easily.

From elementary physics, we know that electric current in a conductor is due to the directed flow of free electrons. When an electric field is applied to the conductor, the free electrons are accelerated in a direction opposite to the electric field. But when these free electrons flow, they collide with the positive atoms of the conductor material. Therefore, there is an opposition in the flow of free electrons. This opposition is referred to as electrical resistance. The property of conductor material by which it opposes the flow of electrons and hence the current is known as resistivity.

In this article, we will discuss electrical resistance and resistivity, their definition, unit, formula, and methods of measurement.

What is Electric Resistance?

When free electrons flow through a conducting material under the influence of an electric field, they collide with positive atoms of the material. Each collision destroys the kinetic energy of electrons. Therefore, electrons face opposition when they flow through the material.

The measure of opposition in the flow of free electrons offered by the material is known as electrical resistance or simply resistance. The resistance is represented by the symbol R.

The circuit component that is used to introduce the electrical resistance in an electrical or electronic circuit is known as a resistor. The resistor is a passive circuit component that only absorbs energy, but does not deliver. The standard circuit symbols of the resistor of resistance R are shown in figure-1.

Formula of Resistance

The following expression gives the empirical formula of electrical resistance −

$$\mathrm{Resistance,\, R=\rho \frac{l}{a}\: \: \cdot \cdot \cdot \left ( 1 \right )}$$

Where, l is the length of the conductor, a is the area of cross-section, and ρ is a constant known as resistivity (or specific resistance) of the conductor material.

The resistance of a conductor can also be determined by Ohm’s law,

$$\mathrm{Resistance,\, R= \frac{V}{I}\: \: \cdot \cdot \cdot \left ( 2 \right )}$$

Where, V is the voltage across the conductor and I is the current through it.

Unit of Resistance

From equation (2), we have,

$$\mathrm{Unit\: of\: resistance= \frac{Volt\, (V)}{Ampere\, (A)}}$$

Thus, the base unit of electrical resistance is volt per ampere (V/A). Although, the practical unit of resistance is Ohm, denoted by the Greek letter Omega (Ω). The unit of resistance was named the Ohm in the honor of Georg Simon Ohm, a German physicist.

We may define the unit of resistance ‘ohm’ as under −

If a voltage of 1 volt across the ends of a conductor wire causes an electric current of 1 ampere to flow through it, then the wire is said to have a resistance of 1 ohm.

Factors Affecting the Resistance

From Equation (1), we can state factors that affect the resistance of a conductor. These factors are as follows−

• The resistance R of a conductor is directly proportional to its length (l) which means if the length of the conductor is increased its resistance will also increase, and vice-versa.

• The resistance R of a conductor is inversely proportional to its cross-sectional area (a). Thus, a thick wire (having a larger cross-sectional area) has less resistance compared to a relatively thin wire.

• The resistance R of a conductor depends upon the nature of the material of which it is made up of. Thus, a conductor with a large value of ρ will have a higher resistance, and vice-versa.

• The resistance R of a conductor also depends upon temperature.

What is Resistivity?

The property of a material by which it opposes the flow of electric current (or electric charge) is known as resistivity. It is also called specific resistance. It is represented by the Greek letter rho (ρ).

From equation (1), the expression of resistivity is given by,

$$\mathrm{Resistivity,\, \rho = \frac{Ra}{l}\: \: \cdot \cdot \cdot \left ( 3 \right )}$$

Thus, the unit of resistivity will be,

$$\mathrm{Unit\: of\: \rho = \frac{\Omega m^{2}}{m}=\Omega m}$$

Hence, the SI unit of resistivity is Ohm-meter (Ω-m).

Therefore, we may also define resistivity as under −

The resistance offered by 1 meter length of wire of a material having a cross-sectional area of 1 m² is known as resistivity or specific resistance of the material.

The resistivity of the conductor depends upon the nature of the material of the conductor, and its temperature. But it is independent of the physical dimension of the conductor.

Measurement of Resistance

The following methods can be used to determine the resistance of a conductor −

• The resistance of a conductor can be measured by using an analog multimeter.

• The resistance of a conductor can also be measured using a digital multimeter.

• The resistance of a conductor can also be determined by Ohm’s law formula. In this method, first, we need to measure the voltage across and current through the conductor. Then, the ratio of two gives the resistance of the wire.

• A device called an ohmmeter can also be used to determine the resistance of a conductor.

Conclusion

In this article, we discussed about the electric resistance and resistivity of a conductor. Resistance is the measure of opposition that a conductor offers in the flow of current, whereas Resistivity is the property of the material of the conductor by which it opposes the flow of current or the movement of electrons. Electrical resistance is one of the most important parameters of an electrical or electronic circuit.