A cylindrical copper wire of length 10m is to be used to carry a steady current of 25A without its temperature rising by more than 40K. The wire is immersed in oil so that all electrical energy produced in it appears as heat absorbed by the oil at a rate not exceeding 35Js−1. The resistivity of copper at the operating temperature may be taken as 1.8×10−8Ωm.
(i) Derive an expression for the radius r of the wire in terms of the given quantities so that the rate of heat production does not exceed 35Js−1.
(ii) Hence calculate the minimum radius and the corresponding cross-sectional area required.
(iii) Discuss qualitatively how using a wire of twice this radius would influence the rate of temperature rise for the same current.