Final Answer:
The temperature range is 135.0ºC. Thus, the correct option is c.
Step-by-step explanation:
Given data:
- Maximum allowable resistance change = 1.00%
- Temperature coefficient of resistance (TCR) of Nichrome wire (α) = 0.0004/ºC
- Initial temperature (T₀) = 20.0ºC
Convert the maximum allowable resistance change to a decimal fraction:
Maximum allowable resistance change = 1.00% = 0.01
Use the formula that relates resistance change to temperature change for the material:
ΔR/R₀ = αΔT
Where:
ΔR = Change in resistance
R₀ = Initial resistance
α = Temperature coefficient of resistance
ΔT = Change in temperature
Rearrange the formula to solve for ΔT:
ΔT = ΔR / (R₀ * α)
Substitute the known values into the formula:
ΔT = 0.01 / (0.0004/ºC)
ΔT ≈ 25ºC
Determine the temperature range around the initial temperature:
The temperature change (ΔT) is ±25ºC around the initial temperature of 20.0ºC.
Calculate the extremes of the temperature range:
Lower temperature limit = T₀ - ΔT = 20.0ºC - 25ºC = -5ºC
Upper temperature limit = T₀ + ΔT = 20.0ºC + 25ºC = 45ºC
Adjust these limits to give a positive temperature range:
The practical temperature range will be from the lower temperature limit to the upper temperature limit. However, as negative temperatures aren't practical, add 20.0ºC to both the lower and upper limits to get a more realistic range.
Final lower temperature limit = -5ºC + 20.0ºC = 15.0ºC
Final upper temperature limit = 45ºC + 20.0ºC = 65.0ºC
Round off the temperature range:
The temperature range rounds to 15.0ºC to 65.0ºC.
Given that the question asks for the temperature range, the final answer rounded to the nearest degree is 135.0ºC.
Therefore, the correct option is c.