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 + αΔT), where RT is the resistance at temperature T, R₀ is the resistance at a reference temperature (here, 0°C), α is the temperature coefficient of resistance, and ΔT is the change in temperature. Given R₀ = 200 Ω, α = 0.004041 °C⁻¹, and ΔT = 80°C, then R80 = 200 * (1 + 0.004041 * 80) = 200 * (1 + 0.32328) = 200 * 1.32328 = 264.656 Ω. Rounded to two decimal places, this is 264.66 Ω, which is closest to 264.65 ohm.
Hint
Use the formula for resistance variation with temperature: RT = R₀(1 + αΔT).