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^(2)`.
The current in the wire is nearly

Options

A. 0.555 A
B. 5.5 A
C. 55 A
D. 550 A

Answer

C

Explanation

Heat dissipated per second `=I^2R`
`I^2R=E`
`I=sqrt((E)/(R ))=sqrt((Epir^2)/(rho_(900)I))=sqrt((231xx.14xx10^-6)/(2.4xx10^-7xx1))approx55A`