Electrical Resistance

DefinitionThe electrical resistance is defined as the difficulty occurs in the flow of electrons. The conductor has free electrons. When the voltage or potential difference is applied across the conductor, the free electrons start moving in the particular direction. During the movement, these electrons collide with the atoms and molecules of the conductor. The atoms or molecules create the obstruction in the flow of electrons. This obstruction is called resistance.

The electrical resistance is provided to the circuit through the resistor. The resistance shows the relation between the applied voltage and the flow of charges. The resistance is inversely proportional to the flow of current

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

Law of Resistance

Every material must possess resistance. The material which has good conductivity have low resistance whereas the material which has low conductivity has high resistance. The ohmmeter measures the electrical resistance. The ohmmeter is connected to the terminal of the circuit whose resistance is to be measured. 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).

earth-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 asearth-resistance-equation

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.

electrical-reistance-equation-2

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

earth-resistance-equation

Also from the above equation, we get,

earth-resistance-equation-1

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

electrical-resistance

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

Specific Resistance of the material

The specific resistance or resistivity is the resistance of the unit length and the unit cross-section area of the material. It is measured in ohmmeter.

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