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 217.3 ΩΩ . What is the temperature on a spring day when the resistance is 215.3 ΩΩ ? Take the temperature coefficient of resistivity for carbon to be ααalpha = −5.00×10−4 C−1C−1 .

24.14 ⁰C

Explanation:

T₀ = initial temperature = 3 °C

R₀ = initial resistance of thermometer at initial temperature = 217.62 Ω

R = Final resistance of thermometer at final temperature = 215.32 Ω

T = final temperature = ?

α = temperature coefficient of resistivity for carbon = - 5.00 x 10⁻⁴ C⁻¹

Final resistance of thermometer at final temperature is given as

R = R₀ (1 + α (T - T₀ ))

Inserting the values

215.32 = 217.62 (1 + (- 5.00 x 10⁻⁴) (T - 3))

T = 24.14 ⁰C

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