Derive expression for specific resistance of a material.

Monjur Alahi

Derive expression for specific resistance of a material.


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Salim Ahmed Kawsar

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At a particular temperature, the resistance (R) of a conductor of uniform cross section is

i. directly proportional to its length (l),

i.e., R ∝ l ……….. (1)

ii. inversely proportional to its area of cross section (A),

R ∝ \(\frac{1}{A}\) ……….. (1)

From equations (1) and (2),

R = ρ\(\frac{l}{A}\)

where ρ is a constant of proportionality and it is called specific resistance or resistivity of the material of the conductor at a given temperature.

iii. Thus, resistivity is given by,

ρ = \(\frac{RA}{l}\)

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