A steady current I flows through a wire of radius r, length L and resistivity `rho`. The current produced heat in the wire. The rate of heat loss in a wire is proportional to its surface area. The steady temperature of the wire is independent of–

Options

A. L
B. r
C. I
D. `rho`

Answer

A

Explanation

`R = (rho l)/A = (rho l)/(pi r^(2))`
Now, `I^(2)R = K2pirl (dT)/(dt)`
`rArr (I^(2)rho l)/(pir^(2)) = K2pirl(dT)/(dt) rArr (dT)/(dt) = (l^(2)rho)/(K2pi^(2)r^(3))`
It is independent of length (l).