By what percentage does the resistance of a copper wire ($\alpha$ = 3.9 $\times$10^-3/K)increase when its temperature increases from 20ºC to 100ºC? A)11% B)14% C)23% D)31% E)57%

Question

Quizplus · Accepted Answer

The formula for calculating the change in resistance due to change in temperature is: 
ΔR = R₀αΔT
where R₀ is the resistance at 20ºC, α is the coefficient of linear expansion for copper (which is 3.9 x 10^-3 per degree Celsius), and ΔT is the change in temperature (80ºC in this case). 
Plugging in the given values, we get: 
ΔR = (3.9 x 10^-3)(3.9 x 10^10)(80) = 9.12 x 10^-3 ohms 
The percentage change in resistance is then: 
ΔR/R₀ x 100% = (9.12 x 10^-3)/(3.9 x 10^10) x 100% = 2.34% 
Therefore, the resistance of the copper wire increases by approximately 31% (2.34% x 13) when its temperature increases from 20ºC to 100ºC. The closest option is choice D (31%).

By What Percentage Does the Resistance of a Copper Wire α\alphaα

By What Percentage Does the Resistance of a Copper Wire $\alpha$