Resistance of a metal wire of length 1 m is `26 Omega` at `20^@ C`. If the diameter of the wire is `0.3 mm`, what will be the resistivity of the metal at that temperature ? Using Table `1.1`, predict the material of the wire.

Explanation

We are given resistance R of the wire `=26 Omega`, the diameter `d=0.3 mm =3xx10^(-4)m`, and the length I of the wire= 1 m. Therefore. From Eq. (12.10), the resistivity of the given metallic wire is `rho=(RA//I0=(RpiD^(2)//4I)`
Substitution of values in this gives
`rho=1.84xx10^(-6)Omega`m
The resistivity of the metal at `20^(@)C "is " 1.84xx10^(-6) Omega`m. From Table 12.2, we see that this is the resistivity of manganese.