Question

What is the resistance of gold wire at 150°C , if it is 25.0 m long with a 0.100 mm diameter and has a resistance of 77.7 Ω at 20.0°C ?

Answer 1

Length of gold wire, L = 25 m, diameter, d = 0.1 times 10^-3 m Resistance, R = 77.7 ohm temperature, T_1 = 20 degree c = 293 K, T_2 = 150 degree c = 423K Resistance, R = rho L/A (rho = resistivity) Resisrance and resistivity depends upon temperature Resistivity, rho = rho_0 (1 + alpha delta T) (alpha = temperature coefficient) = rho_0 (1 + alpha (T-T_0)) Resistance, R = R_0 (1 + alpha(T-T_0)) alpha = 3.4 times 10^-3/degree c Reference at 20 degree c, R_0 = 77.7ohm Reference temperature is the temperature at which alpha is defined. \r\n Resistivity at 20 degree c, rho = RIGTH ARROW /L = 77.7 times 3.14 times (5 times 10^-5)^2 /25 = 2.44 times 10^-8 ohm^-1 rho'= rho_0 (1 + alpha (T - T_0)) = 2.44 times 10^-8 times (1 + 3.4 times 10^-3 (150 degree -20 degree)) = 3.52 times 10^-8 ohm^-1 Resistance, R' = rho' L/A = 3.52