At room temperature (27°C) the resistance of a heating element is 50 . The temperature coefficient of the material is . The temperature of the element, when its resistance is 62 , is

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Solution

Q.
At room temperature (27°C) the resistance of a heating element is 50 $Ω$ . The temperature coefficient of the material is $2.4 \times 10^{- 4^{o}}$ $C^{- 1}$ . The temperature of the element, when its resistance is 62 $Ω$ , is ______ ${}^{o}C$ . [2024]

Ans.
(1027) $R_{0} = 50 Ω;$ $α = 2.4 \times 10^{- 4^{o}}$ $C^{- 1};$ $R = 62 Ω$

$R = R_{0} (1 + α ∆ T)$

$62 = 50 (1 + 2.4 \times 10^{- 4} \times ∆ T)$

$1.24 = 1 + 2.4 \times 10^{- 4} \times ∆ T$

$0.24 = 2.4 \times 10^{- 4} \times ∆ T$

$∆ T = \frac{0.24}{2.4 \times 10^{- 4}} = 1000$

$∴$ Final temperature, $T_{f} = 1000 + 27 = 1027^{o} C$

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