Question

A lamp having tungsten filament consumes $50 \,W$. Assume the temperature coefficient of resistance for tungsten is $4.5 \times 10^{-3}{ }^{\circ} C ^{-1}$ and temperature of the surrounding is $20^{\circ} C$. When the lamp burns, the temperature of its filament becomes $2500{ }^{\circ} C$, then the power consumed at the moment switch is on, is

• A. 608 W
• B. 710 W
• C. 215 W
• D. 580 W

Answer 1

Answer: (A)

Let $R_{0}=$ resistance of filament at room temperature
$R_{t}=$ resistance of filament at $2500^{\circ} C .$
Similarly powers, $P_{0}$ and $P_{t}$
Here, voltage remains the same
$\therefore P_{0}=\frac{V^{2}}{R_{0}}$
Or $R_{0}=\frac{V^{2}}{P_{0}} \text { and } R_{t}=\frac{V^{2}}{P_{t}}$
Also $R_{t}=R_{0}(1+\alpha[2500-20)]$
and $ P_{0} =P_{t}[1+\alpha(2500-20)] $
$=50\left[1+4.5 \times 10^{-3}(2500-20)\right]=608\,W $