Question

The power of a heater is $500\text{W}$ at ${800}^o\text{C}$.

What will be its power at ${200}^o\text{C}$ if $\alpha =4\times {10}^{-4}{}^o{C}^{-1}$?

• A. $611\text{W}$
• B. $576\text{W}$
• C. $672\text{W}$
• D. $484\text{W}$

Answer 1

The correct option is A $611\text{W}$

$P=\frac{V^2}{R}\text{Assuming the source voltage remains the same}$.

$P\propto \frac{1}{R}=\frac{1}{R_0(1+a△T)}$

$R_{800}=R_{200}[1+0.0004(800-200\left)\right]=R_{200}\left[1.24\right]$

Therefore, $\frac{P_{800}}{P_{200}}=$$\frac{R_{200}}{R_{800}}=\frac{1}{1.24}\Rightarrow P_{200}=P_{800}\times 1.24\approx 611W$