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Question: The power of a heater is 500 watt at 800<sup>o</sup> C. What will be its power at 200<sup>o</sup> C ...

The power of a heater is 500 watt at 800o C. What will be its power at 200o C if α6mu=6mu46mu×6mu1046muper6muC\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

611 W

Explanation

Solution

By using P=i2R=V2RP1RP = i^{2}R = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}

P1P2=R2R1=(1+αt2)(1+αt1)500P2=(1+4×104×200)(1+4×104×800)\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)}

500P2=1.081.32611W\frac{500}{P_{2}} = \frac{1.08}{1.32} \Rightarrow 611W