16°C
The equation relating temperature with resistance is given as follows;
[tex]R_{T}[/tex] = [tex]R_{0}[/tex] [[tex]\alpha[/tex]([tex]T^{}[/tex] - [tex]T_{0}[/tex]) + 1] --------------(i)
Where;
[tex]T_{0}[/tex] = Temperature at some reference point
[tex]R_{0}[/tex] = Resistance at the reference point
T = Temperature at some other point
[tex]R_{T}[/tex] = Resistance at the other point
[tex]\alpha[/tex] = constant called "temperature coefficient of the resistor material"
From the question;
Let's take the reference point temperature ([tex]T_{0}[/tex]) as 4.00°C;
Therefore;
[tex]R_{0}[/tex] = Resistance at the reference point = 217.4Ω
[tex]R_{T}[/tex] = Resistance at the other point = 216.0Ω
[tex]\alpha[/tex] = Temperature coefficient of the resistor material (carbon) = -0.0005/°C
Now substitute these values into equation (i) as follows;
216.0 = 217.4 [(-0.0005)([tex]T^{}[/tex] - 4) + 1]
216.0 = 217.4 [-0.0005[tex]T^{}[/tex] + 0.002 + 1]
216.0 = 217.4 [-0.0005[tex]T^{}[/tex] + 1.002]
Divide through by 217.4 as follows;
0.994 = 1.002 - 0.0005T
Solve for T;
0.0005T = 1.002 - 0.994
0.0005T = 0.008
T = 0.008 / 0.0005
T = 16°C
Therefore, the temperature on a spring day at that resistance is 16°C
