10 December 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
        ( a ) Directly proportional to length of conductor ( L )
        ( b ) 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
             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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