By what factor is the resistance of a copper wire changed when its temperature is increased from 30.0°C to 115°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C)−¹. A)1.45 B)1.12 C)1.33 D)0.669 E)4.32

Question

Quizplus · Accepted Answer

The formula to calculate the resistance change due to temperature variation is:

ΔR = R₀αΔT

where:
ΔR = change in resistance
R₀ = initial resistance
α = temperature coefficient of resistivity
ΔT = change in temperature

We are given:
R₀ = resistance at 30°C
α = 3.9 × 10−3 (°C)−1
ΔT = 115°C - 30°C = 85°C

Therefore,
ΔR = R₀αΔT
ΔR = R₀(3.9 × 10−3) (85)
ΔR = 0.3315 R₀

The final resistance (R) will be:
R = R₀ + ΔR
R = R₀ + 0.3315 R₀
R = 1.3315 R₀

Therefore, the resistance increases by a factor of 1.3315 or 1.33 (rounded to two decimal places).
Hence, the answer is (C) 1.33.

By What Factor Is the Resistance of a Copper Wire