Question

A carbon resistor is to be used as a thermometer. On a winter day when the temperature is 4.00 ∘C∘C, the resistance of the carbon resistor is 217.4 ΩΩ . What is the temperature on a spring day when the resistance is 216.0 ΩΩ ?

Answer 1

Answer:

16°C

Explanation:

The equation relating temperature with resistance is given as follows;

$R_{T}$ = $R_{0}$ [$\alpha$($T^{}$ - $T_{0}$) + 1]         --------------(i)

Where;

$T_{0}$ = Temperature at some reference point

$R_{0}$ = Resistance at the reference point

T = Temperature at some other point

$R_{T}$ = Resistance at the other point

$\alpha$ = constant called "temperature coefficient of the resistor material"

From the question;

Let's take the reference point temperature ($T_{0}$) as 4.00°C;

Therefore;

$R_{0}$ = Resistance at the reference point = 217.4Ω

$R_{T}$ = Resistance at the other point = 216.0Ω

$\alpha$ = 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)($T^{}$ - 4) + 1]

216.0 = 217.4 [-0.0005$T^{}$ + 0.002 + 1]

216.0 = 217.4 [-0.0005$T^{}$ + 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