Question

The power of a heater is 500 watt at 800^o C. What will be its power at 200^o C if $\alpha\mspace{6mu} = \mspace{6mu} 4\mspace{6mu} \times \mspace{6mu} 10^{- 4}\mspace{6mu} per\mspace{6mu}{^\circ}C$

• A. 484 W
• B. 672 W
• C. 526 W
• D. 611 W

Answer 1

Answer: (D)

611 W

Answer 2

By using $P = i^{2}R = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}$

⇒ $\frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}} = \frac{(1 + \alpha t_{2})}{(1 + \alpha t_{1})} \Rightarrow \frac{500}{P_{2}} = \frac{(1 + 4 \times 10^{- 4} \times 200)}{(1 + 4 \times 10^{- 4} \times 800)}$

⇒ $\frac{500}{P_{2}} = \frac{1.08}{1.32} \Rightarrow 611W$