Answer to Question #276414 in Electric Circuits for Rex

Question

It is found that the resistance of a coil of wire increases from 40 ohm at 15°C to 50 ohm at 60°C. Calculate the resistance temperature coefficient at 0°C of the conductor material.

Answer 1

$R_1 = 40 \; ohm \\ R_2 = 50 \; ohm \\ T_1 = 15 \;°C \\ T_2 = 60 \; °C \\ R = R_0(1+αΔT) \\$

R₀ = resistance at 0 °C

α = resistance temperature coefficient

$R_1 = R_0(1+α(T_1-0)) \\ 40 = R_0(1+15 α) \\ 50 = R_0(1+60 α) \\ \frac{40}{50} = \frac{1+15α }{1+60α } \\ 4 + 240 α = 5 + 75 α \\ 165 α = 1 \\ α = 6.06 \times 10^{-3} \; 1/°C$