Question

A lamp having tungsten filament consumes $50W$. 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 $P_0=P_t[1+\alpha (2500-20)]$
$=50\left[1+4.5\times 10^{-3}(2500-20)\right]=608W$