Define resistivity or specific resistance ?

Specific resistance, also known as resistivity, is a fundamental property of a material that quantifies how strongly it opposes the flow of electric current. It is defined as the resistance offered by a conductor of unit length and unit cross-sectional area.

Formula for Specific Resistance

The mathematical representation of specific resistance (ρ) is given by:

ρ = R × A / l

Alternatively, for a cylindrical wire of radius r, the formula can be expressed as:

ρ = R × π × r2 / l

Here:

• ρ is the specific resistance (resistivity).
• R is the resistance of the material.
• A is the cross-sectional area of the conductor.
• l is the length of the conductor.
• r is the radius of the wire (if cylindrical).

Unit of Specific Resistance

The unit of specific resistance in the SI system is ohm-meter (Ω·m).

Dimensional Formula

The dimensional formula of specific resistance is:

[M1 L3 T-3 A-2]

Significance of Specific Resistance

Specific resistance is crucial in determining the suitability of a material for electrical applications. Materials with low specific resistance, such as copper and aluminum, are excellent conductors, while those with high specific resistance, such as rubber and glass, are good insulators.

Understanding specific resistance is essential in designing electrical circuits, selecting materials for wiring, and optimizing energy efficiency.