The formula for resistivity is: ρ = R A L where ρ is resistivity, R is resistance, A is cross-sectional area, and L is the length of the conductor.We can see from the formula that A and L are involved, why then does resistivity not depend on dimensions?

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The formula for resistivity is:  ρ  =            R      A        L  where   ρ is resistivity,   R is resistance,   A is cross-sectional area, and   L is the length of the conductor.We can see from the formula that   A and   L are involved, why then does resistivity not depend on dimensions?

verdesett014ci · Accepted Answer

It&#039;s because resistance (  R) is also a function of size.A short and wide section of a material will have lower resistance than a long thin section of the same material. Larger cross sections have less resistance, and longer conductors have more resistance.Therefore, by multiplying resistance by area and dividing by length, you get a value for a material property (resistivity   ρ) that doesn&#039;t depend on the size of the conductor.That is the point of resistivity, to be applicable to a material over various cross sections and lengths.

Ainsley Zimmerman · Accepted Answer

True, A and L are involved. But resistivity is a constant.In the equation  ρ  =            R      A        L  if you change the resistance and length of conductor and then experimentally measure the resistance, and put it in the formula, you&#039;ll find that the resistivity has remained a constant for all different A and L, because R gets suitable modified to keep resistivity constant.This is an experimental result. I remember trying this out myself, and the results showed that resistivity is a constant.For another example, consider this formula for Coloumb&#039;s law:  F  =      1          4      π              ϵ        0                                q        1                    q        2                    r      2      where       ϵ    0   is the permittivity of free space. Now, you can aptly write      ϵ    0    =      1          4      π      F                          q        1                    q        2                    r      2      and say that it is not a constant. But experiments show that for different values of       q    1  ,       q    2   and   r, the force   F varies such that permittivity       ϵ    0   remains a constant for a particular material, at a particular temperature.

The formula for resistivity is: ρ = R A </mro

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