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Question
At room temperature (27.0°C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is 1.70 × 10−4 °C−1.
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Solution
Given: Initial temperature, T1 = 27°C
Initial resistance, R1 = 100 Ω
Let T2 is the increased temperature of the filament.
Final resistance, R2 = 117 Ω
The temperature coefficient of the material of the filament,
α = 1.70 × 10−4 °C−1
α is given by the relation,
α = `(R_2 - R_1)/(R_1(T_2 - T_1))`
`T_2 - T_1 = (R_2 - R_1)/(R_1α)`
`T_2 - 27 = (117 - 100)/(100 xx 1.7 xx 10^-4)`
`T_2 - 27 = 17/(170 xx 10^-4)`
`T_2 - 27 = 17/(0.017)`
T2 − 27 = 1000
T2 = 1000 + 27
∴ T2 = 1027°C
Therefore, at 1027°C, the resistance of the element is 117 Ω.
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