A small bulb is rated at 7.50 W when operated at 125 V.The tungsten filament has a temperature coefficient of resistivity $\alpha$ = 4.50*10 ^- ³ / $\degree$C.When the filament is hot and glowing,its temperature is seven times room temperature (20 $\degree$C).What is the resistance of the filament (in ohms)at room temperature? A)234 B)1 350 C)2 080 D)4 530 E)5 630

Question

Quizplus · Accepted Answer

The power rating and voltage can be used to find the resistance when the bulb is operating: R_hot = V^2 / P = (125^2) / 7.50. The temperature of the filament when hot is 7 times room temperature, so T_hot = 7 * 20°C = 140°C. Using the temperature coefficient of resistivity, the resistance at room temperature can be calculated: R_room = R_hot / (1 + α * (T_hot - T_room)). Solving this gives approximately 234 ohms.

A Small Bulb Is Rated at 7 α\alphaα = 450*10 - 3

A Small Bulb Is Rated at 7 $\alpha$ = 450*10 ^- ³