A wire has resistance 100 ohm at 0 C and 200 Ohm at 100 C. What is its temperature coefficient in K-1?
Correct answer: C. 0.01
- A. -0.01
- B. -1/273
- C. 0.01
- D. 1/273
Explanation
(The mcq option seem incorrrect, the only explanation possible is as follows;)Given that,Resistance at 0°C = 100ΩResistance at 100°C = 200ΩWe have to find temperature coefficient of wire in Kˉ¹Resistance of conductor depends on the length of conductor, area of cross-section of conductor and temperature.Using the Formula,ΔR = R × α × ΔT where,'ΔR' denotes change in resistance'R' denotes initial resistance'α' denotes temperature coefficient'ΔT' denotes change in temperatureInitial temperature = 0°C = 273KFinal temperature = 100°C = 373KΔR = R × α × ΔT(R₂ - R₁) = R₁ × α × (T₂ - T₁)(200-100) = 100 × α × (373-273)100 = 100 × α × 100α = 1/100α = 1 × 10ˉ² Kˉ
This question appeared on the UHS MDCAT 2008 paper, which you can sit online with every answer explained.
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About Temperature Coefficient of Resistivity
Temperature coefficient of resistivity describes how a material's resistivity changes for each degree change in temperature. Questions use the relation between resistance, temperature and the coefficient, especially for metallic conductors with positive values and semiconductors with negative values. Resistivity is a material property, unlike resistance, which also depends on dimensions.
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