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2015-07-30T22:26:00+05:30

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R =  ρ  L / A

Resistance of a wire is proportional to the length of the conductor/resistor wire.  Then the resistance of the wire is inversely proportional to the area of cross section.. Because the bigger the cross section, there is more area and more number of electrons available for flow of electricity.  So resistance is less proportionately.

Thus  R  is proportional to  L / A.
The constant of proportionality is found to be constant and specific property for any material.  That is called  the resistivity ρ  of the material.

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in potentiometer the wire used is managanin wire whose resistivity is high.but in potentiometer the wire used must be of low resistance so can we say that resistance and resistivity are inversely proportional?
when we resistivity is high or low, it is comparing against other metals, alloys... but R = ρ L / A.. L is say 1 meter.. A = 0.02 m^2 then R is 25 micro ohm.. That is very small resistance.. ρ is of the order of 10 power -6