A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−³ (°C)−¹ will have what resistance at 95°C? A) 17 Ω B) 19 Ω C) 31 Ω D) 24 Ω E) 7 Ω

Question

Quizplus · Accepted Answer

Using the formula for temperature dependence of resistivity, we have:

ΔR/R = αΔT, where ΔR/R is the fractional change in resistance, α is the temperature coefficient of resistivity, and ΔT is the change in temperature.

ΔR/R = (3.9 × 10−3 (°C)−1) × (95°C − 25°C) = 0.273

Therefore, the increase in resistance is:

ΔR = (ΔR/R) × R = (0.273) × (24 Ω) = 6.552 Ω

So the final resistance at 95°C is:

Rf = R + ΔR = 24 Ω + 6.552 Ω = 30.552 Ω ≈ 31 Ω

Hence, the best choice is C.

A 24-Ω Platinum Wire at 25°C with a Temperature Coefficient