Law of Resistance

Resistance

• It is a defined as property of substance which oppose the flow of current through it. 
• The SI unit of resistance is ohm ( Ω ). 
• One ohm is defined as the resistance of conductor when one voltage applies between conductor resulting one ampere current flows through it. 
• The resistance is expressed in milli – ohm , kilo ohm or mega ohm.

Law of resistance

• The resistance of conductor depends upon length of the conductor, area of conductor, type of conductor material and operating temperature.
• The resistance of the conductor is

        ( 1 ) Directly proportional to length of conductor ( L )

        ( 2 ) Inversely proportional to area of the conductor ( a )

        R a ( L / a )

        R = ρL / a

Where ρ = Resistivity of the material or specific resistance of the material

Unit of Resistivity

        ρ = Ra / L

           = ohm – meter² / meter

           = ohm – meter

• The unit of resistivity is ohm – meter.

Specific Resistance

• If we consider a = 1 meter² and L = 1 meter, the resistance is equal to specific resistance.
• The specific resistance of a material is defined as a resistance of material having unit length and unit cross section area.

                                   OR

• It is defined as the resistance between opposite faces of unit cube material.

Conductance

• It is defined as reciprocal of resistance. 
• The symbol of conductance is G. Its unit is ohm^-1 or mho. 
• The other unit is Siemens ( S ). 
• The conductance is defined as inducement offered by the conductor for the flow of current.

Conductance G = 1 / R

                         = 1 / ( ρL / a )

                         = a / ρL

                        =  ( 1 / ρ )( a / L )

                        =  σa / L

Conductivity

• The σ ( sigma ) is called as specific conductance or conductivity of the material. 
• Therefore the conductivity is reciprocal of resistivity or specific resistance. 
• The unit of conductivity is siemen / meter.

       G = σa / L

       σ = GL / a

          = Siemen – meter / meter²

          = Siemen / meter

You may also like :

Ideal voltage source and Ideal current source

Working of Auto transformer and saving in copper

Transformer as constant flux device

Characteristic of DC Generator

Practical DC Generator