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 12.2, predict the material of the wire.

Explanation

We are given the resistance R of the wire = 26 `Oemag `, the diameter d = 0.3 mm` = 3 xx 10^(-4)` m, and the length l of the wire = 1 m .
Therefore, from Eq. (12.10), the resistivity of the given metallic wire is `rho = (RA //l) = ( Rpi d ^2 // 4l)`
Substitution of values in this gives
`rho = 1.84 xx 10^(-8) Omega m`
The resistivity of the metal at `20^@ C `is `1.84 xx 10^(-8) Omega ` m. From Table 12.2, we see that this is the resistivity of manganese.