10/12/2017

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

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