A platinum-resistance thermometer has a resistance of 10 ω at 0°C and 18 ω at 100°C. Assuming that resistance…

Analyze the question: The resistance changes uniformly (linearly) with temperature. We know R at 0°C and at 100°C, and we need R at 45°C.

Concept: For linear variation, the change in resistance is proportional to the change in temperature:

R_θ = R₀ + (R₁₀₀ − R₀) × (θ / 100)

Solution:

• R₀ = 10 Ω
• R₁₀₀ = 18 Ω
• Total change over 100°C = 18 − 10 = 8 Ω
• Change per °C = 8/100 = 0.08 Ω/°C
• Change at 45°C = 0.08 × 45 = 3.6 Ω

R₄₅ = 10 + 3.6 = 13.6 Ω

Note on option E (3.6): This is the increase in resistance, not the resistance itself. It is a common trap, so always add the change to the starting value of 10 Ω.

Exam tip: For "uniform change" questions, use the ratio method: (R_θ − R₀)/(R₁₀₀ − R₀) = θ/100. Here: (R − 10)/8 = 45/100, so R − 10 = 3.6 and R = 13.6 Ω.