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Relationship between Resistance and its physical dimensions

As conductor is made up of some material that will have certain dimensions such as length and area etc that plays a part in calculating the resistance. The resistance of a conductor depends on the following parameters
1:Length of conductor 2:Cross-sectional area of conductor 3:Resistivity  4:Temperature of the conductor
Now we will explain all of above four parameters one by one.

Length and Area of conductor :

The resistance of material is directly proportional to the length of the conductor but inversely proportional to the area of the conductor. We know that when length of a material increases its area will decrease which means path or channel through which electrons flow will decrease. Under such a condition more collision will occur resulting in increase of resistance.Mathematically,
                                     
                                                        RαL .......(1)
                                      Rα1/A ........(2)
 By combining above (1) & (2)
                                                        RαL/A
                                           R=ρL/A
where ρ=proportionality constant and is called resistivity.

Resistivity:

It is defined as 

 "The nature of composition of the material from which a conductor is made is called resistivity of the material."
It is also called specific resistance of the material as every material has an inherit unique resistance.

Unit:


The unit of resistivity is ohm meter.

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