Answer to Question #167036 in Electric Circuits for Richard

Question

Some aluminum wire has a resistance of 50 Ω at 20 ℃. The wire is heated to a temperature of 100 ℃. Determine the resistance of the wire at 100 ℃, assuming that the temperature coefficient of resistance at 0℃ is 1/250 per ℃?

Answer 1

$R_{20} = 50\varOmega, \space \space \alpha_o = 0.004/^oC \space \space \space \space and \space \space \space \space \large\frac{R_{20}}{R_{100}} = \frac{[1+\alpha_o(100)]}{[1+\alpha_o(20)]}$

Hence, $R_{100} = \large\frac{R_{20}[1+100\alpha_o]}{1+20\alpha_o} = \frac{50[1+100(0.004)]}{[1+20(0.004)]} = \frac{50[1+0.40]}{[1+0.08]}=\frac{50*1.40}{1.08}$ $= 64.8\varOmega$