Derive expression for specific resistance of a material.

1.	Derive expression for specific resistance of a material.
Answer» 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 = \(\frac{RA}{l}\)

Answer»

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 = \(\frac{RA}{l}\)

Discussion