Problem 18: The resistance of a tungsten wire used in a filament of a 60W bulb is 240Ω when a bulb is hot at a temperature of 2020^oC what would you estimate its resistance at 20^oC?

Solution:

Step: 1 Overview

See overview of problem 17.

Step: 2 Calculation

Value of alpha for tungsten is 0.0046. In order to find resistance at 20^oC, we first find R_o. We know that:

R_t=R_o(1+αt)
R₂₀₂₀=R_o(1+(0.0046)(2020))
240=R_o(1+9.292)
240=R_o(10.292)
R_o=240/10.292
R_o=23.32Ω

After finding R_o, now we'll find the resistance at 20^oC:

R_t=R_o(1+αt)
R₂₀=(23.32)(1+(0.0046)(20))
R₂₀=(23.32)(1+0.092)
R₂₀=(23.32)(1.092)
R₂₀=25.47Ω (Ans)