Resistance of a metal wire of length 1m is `26 Omega" at " 20^@C`.If the diameter of the wire is 0.3mm, what will be the resistively fo the metal at that temperature ? Using Table 2 (on page 116), predict the material of the wire.

Explanation

We are given the resistance R of the wire = 26`Omega`, the diameter d = 0.3 mm `= 3 xx 10^(-4) m, ` and the length l of the wire = 1 m.
Therefore, from equation `R =rho =l/A` the resistively of the given metallic wire is
`rho = (RA)/l`
`=(R pi d^2//4l) ( :. A = pi r^2 = pi(d/2)^2 =(pid^2)/4)`
`:. rho =(26xx 3.14 xx (3 xx 10^(-4))^2)/(4 xx 1)`
`rho = 1.84 xx 10^(-6) Omega m`
The resistivity of the metal at `20^@C` is `1.84 xx 10^(-6) Omega m`.
From Table 2 (on page 116), we see that this is the resistivity of manganese.