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 conductor changes with temperature according to the formula: RT = R0 × (1 + α × ΔT), where RT is the resistance at temperature T, R0 is the resistance at reference temperature T0, α is the temperature coefficient of resistance, and ΔT is the change in temperature (T - T0).Given: R0 = 200 Ω (at T0 = 0°C), α = 0.004041 °C⁻¹, T = 80°C.ΔT = 80°C - 0°C = 80°C.R80 = 200 × (1 + 0.004041 × 80) = 200 × (1 + 0.32328) = 200 × 1.32328 = 264.656 Ω. This matches option A.
Hint
Use the formula for resistance variation with temperature: RT = R0(1 + αΔT).