A wire of length 1 m and radius `10^-3`m is carrying a heavy current and is assumed to radiate as a black body. At equilibrium, its temperature is 900 K while that of surrounding is 300 K. The resistivity of the material of the wire at 300 K is `pi^@xx10^-8` ohm m and its temperature coefficient of resistance is `7.8xx10^(-3)//C` (stefan's constant`sigma=5.68xx10^-8W//m^(2) K^(4)`).
Q. The resistivity of wire at 900 K is nearly

Options

A. `2.4xx10^7ohmm`
B. `2.4xx10^-7ohmm`
C. `1.2xx10^-7ohmm`
D. `1.2xx10^-7ohmm`

Answer

B

Explanation

`rho_(300)=pi^2xx10^-8ohmm`
`rho_(900)=(rho_(300)(1+900alpha))/((1+300alpha))`
`=(pi^2(10^-8)(1+900xx7.9xx10^-3))/((1+300xx7.8xx10^-3))`
`=pi^2xx10^-8xx(8.02)/(3.34)`
`=2.4pi^2xx10^-8`
`approx2.4xx10^-7ohmm(pi^2approx10)`