Question Detail
Question
A copper coil has a resistance of 200 ohms when its mean temperature is 0 degree centigrade. Calculate the resistance of the coil when its mean temperature is 80 degree centigrade. Temperature coefficient of copper is 0.004041 centigrade-1.
Correct Answer
Option A is the correct answer.
Detailed Explanation
The resistance of a material changes with temperature according to the formula: Rt = R0(1 + αΔT), where Rt is the resistance at temperature t, R0 is the resistance at reference temperature (0°C in this case), α is the temperature coefficient of resistance, and ΔT is the change in temperature.Given: R0 = 200 Ω, α = 0.004041 °C-1, ΔT = 80 °C - 0 °C = 80 °C.R80 = 200(1 + 0.004041 × 80)R80 = 200(1 + 0.32328)R80 = 200 × 1.32328R80 = 264.656 Ω.Rounding to two decimal places, the resistance is 264.66 Ω, which matches option A.
Hint
Use the formula for resistance variation with temperature: Rt = R0(1 + αΔT).