Electrical Resistance

Definition: Electrical resistance is defined as the opposition offered to the flow of current (free electrons). When the potential difference is applied across a conductor, the free electron starts moving in a particular direction. While moving through the material, these electrons collide with other atoms and molecules. They oppose this flow of electrons through it. This opposition is called resistance.

Unit: Resistance is measured in ohms (kilo-ohms) and is denoted by symbols (or kῼ). A wire is said to have a resistance of one ohm If one-ampere current is passed through it.

Law of Resistance

The resistance of the wire depends on the following factors. These factors are:

  • The resistance of a wire is directly proportional to its length, l, i.e., R ∝ l.
  • The resistance of the wire is inversely proportional to its area of cross section (a).

resistance-equation-1

Where ρ is a constant of proportionality also called the resistivity of the wire material. The values of ρ depend on the nature (atomic structure) of the materials.

  • The resistance of the wire depends on the nature (atomic structure) of the material of which the wire is made.
  • The resistance of the wire depends on the temperature of the wire.

Resistivity of the Material

The resistivity of the material is defined as the resistance offered by the one-meter length of wire (of given area) having an area of cross section of one square meter. The resistance of the wire is given as

resistance-equation-2

If, l = 1 meter; a = 1 m2 then the resistance of the wire is R = ρ

In place of wire, if a cube of the one-meter side of a given material is taken and their two opposite faces are considered, then the resistance is given by the relation shown below.

resistance-equation-3

Hence, the resistance offered between the two opposite two faces of the one-meter cube of the given material is called the resistivity of the material.

Unit: Resistance of the wire is given by the equation

resistance-equation-2

Also from the above equation we get,

resistance-equation-4

Substituting the units of various quantities as per SI units, we get,

resistance-equation-5

Hence the unit of resistivity is ohm-meter in SI units.

Specific Resistance of the material

The resistance of the material is also known as specific resistance of that material. The specific resistance of the material represents the resistance of a material having specific dimensions, i.e., 1-meter length and 1 square meter area of cross-section.
Hence, the specific resistance of material is defined as the resistance of the material having specific dimensions, i.e., one-meter length and one square meter of an area of cross-section.

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