Q. A lamp having tungsten filament consumes 50 W. Assume the temperature coefficient of resistance for tungsten is $4.5 \times 10^{- 3}℃^{- 1}$ and temperature of the surrounding is $20℃$. When the lamp burns, the temperature of its filament becomes $2500℃$ , then the power consumed at the moment switch is on, is
A) 608 W
B) 710 W
C) 215 W
D) 580 W
Explanation
(a) Let $R_{0}$ = resistance of filament at room temperature
$R_{t}$ = resistance of filament at 2500$℃$
Similarly powers, $P_{0}\ and\ P_{t}.$
Here, voltage remains the same.
${\ P}_{0} = \frac{V^{2}}{R_{0}}$
or ${\ R}_{0} = \frac{V^{2}}{P_{0}},\ \ \ R^{t} = \frac{V^{2}}{P_{t}}$
also $\ R_{t} = R_{0}\left\lbrack 1 + \alpha(2500 - 20) \right\rbrack$
and ${\ P}_{0} = P_{t}\lbrack 1 + \alpha(2500 - 20)\rbrack$
$\ = 50\lbrack 1 + 4.5 \times 10^{- 3}(2500 - 20)\rbrack$
= 608W
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.