By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C)−¹. A) 1.43 B) 1.14 C) 1.29 D) 0.71 E) 3.93

Question

Quizplus · Accepted Answer

First, we need to calculate the change in temperature:

ΔT = 110°C - 35°C = 75°C

Next, we use the temperature coefficient of resistivity for copper to calculate the change in resistance:

α = 3.9 × 10−3 (°C)−1

ΔR/R = α ΔT

ΔR/R = (3.9 × 10−3 (°C)−1) (75°C)

ΔR/R = 0.2925

Finally, we calculate the factor by which the resistance changes:

R2/R1 = 1 + ΔR/R

R2/R1 = 1 + 0.2925

R2/R1 = 1.2925

Therefore, the resistance of the copper wire changes by a factor of 1.2925 when its temperature is increased from 35°C to 110°C, which is closest to choice C (1.29).

By What Factor Is the Resistance of a Copper Wire