At room temperature (27.0 °C) the resistance of a heating elementis 100 W. What is the temperature of the element if the resistance isfound to be 117 W, given that the temperature coefficient of thematerial of the resistor is 1.70 × 10–4 °C–1.

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Solution

It is given that the resistance of a heating element at room temperature, R=100Ω and the temperature coefficient of the material of the resistor, α=1⋅70× 10 − 4 0 C −1 .

The formula of temperature coefficient is,

α= R 1 −R R( T 1 −T )

Substitute the values.

1⋅70× 10 −4 = 117−100 100( T 1 −27 ) T 1 −27=1000 T 1 =1027 °C

Thus, the value of the temperature of the element for the resistance of 117Ω is

1027 °C.

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