The wire of a platinum resistance thermometer has d resistance of 3.5 at 0 °C and 10.52 at 100°C. Calculate the temperature of the wire when its resistance is 7.5.

Correct Answer is : 57 ∘^{}∘C

Correct Answer is : 57 ∘^{}∘C

Test Index

WAEC Physics 2019 Paper

Question : 18

Total: 49

\Omega

\Omega

\Omega

Solution:

Concept:

A platinum resistance thermometer relates resistance to temperature by a linear relation between

0\,{}^\circ\text{C}

and

100\,{}^{\circ}\text{C}

Explanation:

Let

R_0

be the resistance at

0\,{}^{\circ}\text{C}

Let

R_{100}

be the resistance at

100\,{}^{\circ}\text{C}

Given:

R_0 = 3.5\,\Omega

and

R_{100} = 10.52\,\Omega

The resistance of the wire is

R = 7.5\,\Omega

Use the temperature formula:

t = \frac{R - R_0}{R_{100} - R_0} \times 100\,{}^\circ\text{C}

Substitute the values:

t = \frac{7.5 - 3.5}{10.52 - 3.5} \times 100

t = \frac{4}{7.02} \times 100

t = 56.98\,{}^{\circ}\text{C}

So,

t \approx 57\,{}^{\circ}\text{C}

Answer:

The temperature of the wire is

57\,{}^{\circ}\text{C}

, which is option D.

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