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)1350
C)2080
D)4530
E)5630

Question

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)1350
C)2080
D)4530
E)5630

Quizplus · Accepted Answer

The resistance at room temperature can be calculated using the formula $ R = \frac{V^2}{P} $ for the hot filament, and then adjusting for temperature using $ R_0 = \frac{R}{1 + \alpha \Delta T} $. Solving gives approximately 234 ohms.

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

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