Discussion
The power of a heater is 500 W at 800 °C . What will be its power at 200 °C if temperature coefficient of resistance is 4 × 10-4 / °C ?
Answer: A
The power at 200 °C is about 611 W.
At constant supply voltage the power is \(V^{2}/R\), so it is inversely proportional to the resistance. With the temperature coefficient referred to 0 °C, \(R_{t} = R_{0}(1 + \alpha t)\).
\[ \begin{aligned} R_{800} &= R_{0}(1 + 0.32) = 1.32R_{0} \\ R_{200} &= R_{0}(1 + 0.08) = 1.08R_{0} \\ P_{200} &= 500 \times \frac{1.32}{1.08} = 611\ \text{W} \end{aligned} \]
The resistance is lower at the lower temperature, so the power must be higher than 500 W, which rules out 526 W as too small a change; 672 W and 620 W do not follow from the ratio of resistances.
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