Laws of Resistance and Specific Resistance

The laws of resistance states that the Resistance “R” offered by a conductor depends upon following factors: The resistance of conductor is the obstruction posed by the conductor to the flow of current through it.

1. The Resistance “R” is directly proportional with it’s length “L”

2. The Resistance “R” is Inversely proportional with it’s Cross Sectional Area: “A”

3. The Resistance “R” is dependent on the Nature of the material.

4. The Resistance “R” is dependent on the Temperature of the conductor.

Note:- It is found that among physical factors Temperature plays the most significant factor in determining the resistance  but other physical factors like Pressure and Tension also effect the resistance of a substance.

Laws of resistance
Laws of resistance

 

Resistivity or Specific Resistance:

If we do not change the temperature of the conductor or neglect it’s effect then we can come into conclusion that:

The resistance of a substance is directly proportional to it’ length divided by it’s cross sectional area.

Or, R \propto \dfrac{L}{A}

or, R = \rho \times \dfrac{L}{A}  , where \rho is a constant depending on the nature of the material of the conductor and is known as it’s Specific Resistance or Resistivity.

When L = 1 Meter and A = 1 Meter square Or when the material takes in of length 1 meter and it’s cross sectional area is one meter square as shown on the figure below then , R = \rho

specific resistance
specific resistance

So the specific resistance of a substance can be defined as the resistance between the opposite faces of a meter cube of that material.

 

Formula and Unit of Specific Resistance:

From the equations derived above we can derive the formula for resistivity as:

\rho = \dfrac{AR}{L}

So , the unit of resistivity is : Ohm Meters or \Omega m