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

Explanation

Given the resistance of the wire `R = 26Omega`, the diameter `d = 0.3 mm= 3 xx 10^(-4)` m, and the length of the wire l =1 m.
The resistivity of the given metallic wire is
`rho= (RA)/(l)= (Rpid^(2))/(4l)`
`= (26 xx 22 xx 3 xx 10^(-4) xx 3 ^(-4))/( 7 xx 4xx 1)= 183.857 xx 10^(8)`
`1.84 xx 10^(-6)Omegam`
The resistivity of the metal at `20^(@)C` is `1.84 xx 10^(-6)Omegam`