Question

Two wires of different materials x and y have resistances per unit lengths, 100 Ω(km)^-1, 50 Ω(km)^-1 and temperature coefficients 0.0025 (°C)^-1, 0.00075 (°C)^-1 respectively. It is desired to make a coil having 1000Ω resistance and a temperature coefficient of 0.001 (°C)^-1 by using suitable lengths of the two wires in series. Calculate their respective lengths in metre.

Answer 1

Let R_x and R_y be the respective resistances at a given temperature. The total resistance after a charge ΔT becomes

As 0.001(°C)^-1 is the temperature coefficient of the combination, we also have