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

16°C

Step-by-step 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