# Difference between Resistance and Reluctance

In electrical engineering, there are two important terms resistance and reluctance related to electromagnetic circuits such as motor, generator, transformer etc. Where, the resistance is the parameter of circuit which is regarded to electric current, whereas the reluctance is the parameter regarded to the magnetic flux in the circuit.

In this article, we will highlight all the significant differences between resistance and reluctance by considering different parameters such as basic definition, unit, denotation, affected quantity, etc. Let's start with some basics of Resistance and Reluctance so that it becomes easy to understand the differences between them.

## What is Resistance?

Resistance or electrical resistance is defined as the measure of opposition offered by a substance in the path of electric current. The resistance is denoted by the symbol ‘R’ and is measured in Ohms (Ω).

When an electric current flows through a material, the material opposes the flow of the current and results in the rise in temperature. Therefore, the resistance is nothing but electric friction. In the nature, every matter has a certain amount of resistance. The value of the resistance depends on the type of material. Since, in electrical and electronics engineering, we come across three types of materials namely conductor, semiconductor and insulator.

The conductors (or metals) offer least resistance in the flow of current, while the insulators possess highest resistance in the path of current flow. The semiconductors are those materials whose resistance lies between the resistance of conductors and insulators.

The experimental formula of the resistance of a wire is given by the following expression,

$$R\:=\:\rho\frac{l}{A}$$

Where, ρ is the resistivity or specific resistance, l is the length of wire and A is the area of cross-section of the wire.

Therefore, from this equation, we can state the factors affecting the resistance of a material or wire, which are as follows:

• The resistance of a wire is directly proportional to the length of wire.
• The resistance is inversely proportional to area of cross-section of the wire.
• The resistance depends on the nature of material.

In practice, the resistance of a material is used to design different types of electrical devices such as electric iron, line insulators, heater, bulb, etc.

## What is Reluctance?

The measure of opposition offered by a substance in the path of flow of magnetic flux is called the reluctance of the material. The reluctance is denoted by the symbol ‘S’ and is measured in ampere-turn per weber (AT/Wb) or 1/Henry. The reluctance is also known as magnetic reluctance, magnetic resistance or magnetic insulation.

The magnetic reluctance is the physical quantity which is related to a magnetic or electromagnetic circuit. The reluctance of the magnetic circuit depends on the length and area of the circuit. Where, it is directly proportional to the length and inversely proportional to the area of cross-section. Therefore, we can express the reluctance of a magnetic circuit as

$$S\:=\:\frac{l}{\mu\:A}\:=\:\frac{l}{\mu_o\:\mu_r\:A}$$

Where, l is the mean length of magnetic circuit, A is the area of cross-section and μ is the permeability of the material.

The magnetic reluctance finds applications in the electromagnetic devices such as transformers, generators, motors, measuring instruments, etc. It reduces the effect of magnetic saturation in a magnetic circuit.

## Difference between Resistance and Reluctance

Both Resistance and Reluctance are Analogous quantities related to electromagnetic circuits, however, there are several noticeable differences between Resistance and Reluctance that are given in the following table:

Basis of Difference Resistance Reluctance
Definition The measure of opposition in the path of flow of electric current offered by a substance is known as resistance. The measure of opposition in the path of flow of magnetic flux offered by the substance is known as reluctance.
Alternate name Resistance is also called electric friction. Reluctance is also known as magnetic resistance or magnetic friction.
Denotation Resistance is usually denoted by the symbol ‘R’. Reluctance is usually denoted by the symbol ‘S’.
Regarded circuit Resistance is the circuit parameter related to the electric circuits. Reluctance is the circuit parameter related to the magnetic circuits.
Formula The resistance of any conductor wire is calculated by using the following formula: $$R\:=\:\frac{\rho\:l}{A}$$ The reluctance of a magnetic circuit is calculated by using the following formula: $$S\:=\:\frac{l}{\mu\:A}$$
Relation with current The following expression shows the relation between resistance and current − $$R\:=\:\frac{V}{I}$$

Where, V is voltage and I is current.

The relation between reluctance and current is given by, $$S\:=\:\frac{NI}{\phi}$$

Where, N is the number of turn in electromagnetic coil and φ is the magnetic flux.

Unit of measurement Resistance is measured in Ohm (Ω). It may also be measured in volt per ampere (V/A). $$1\Omega\:=\:1VA^{-1}$$ Reluctance is measured in Ampere- Turns per Weber (AT/Wb) or 1/Henry.
Primary function The main function of the electric resistance is to limit the electric current flowing in the circuit. The main function of the magnetic reluctance is to limit the value of magnetic flux flowing in a magnetic circuit.
Reciprocal The reciprocal of resistance is called the conductance (G). Which is the measure of ease in the flow of electric current. The reciprocal of reluctance is called permeance (P). Which is the measure of ease in the flow of magnetic flux.
Effect of temperature The resistance of a material greatly changes with the change in temperature. The reluctance of the material comparatively less affected by the change in temperature.
Change with AC and DC Resistance of a material does not change with the AC or pulsating DC. Reluctance of a material changes with the AC and pulsating DC. Where, it pulsates at the same frequency as that of the supply.
Value in air medium Resistance of air is ideally infinity. Which means no electric current can flow through air. Reluctance of air is very high, but not infinity. Which means air allows the flow of magnetic flux.
Loss Resistance opposes the flow of electric current and results in the loss of power in the form heat. Reluctance opposes the flow of magnetic flux, but instead of dissipating it in the form of heat, it stores in the form of magnetic field.
Applications Resistance is used to design many electrical appliances such as electric iron, heater, bulb, etc. Reluctance is used in various electromagnetic devices like transformer, generator, motor, etc. It is used to reduce the magnetic saturation of a magnetic core.

## Conclusion

The most significant difference that you should note here is that Resistance is the measure of opposition in the flow of electric current, while Reluctance is the measure of opposition in the flow of magnetic flux.