A small bulb is rated at 7.50 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 4.50 × 10⁻³ / °C. When the filament is hot and glowing, its temperature is seven times room temperature (20 °C). What is the resistance of the filament (in ohms) at room temperature?

Question

Quizplus · Accepted Answer

The power rating and voltage give the resistance when hot: R_hot = V^2 / P = (125^2) / 7.50 = 2083.33 ohms. The temperature when hot is 7 times room temperature: T_hot = 7 * 20 = 140 °C. Using the temperature coefficient of resistivity, R_room = R_hot / (1 + α * (T_hot - 20)) = 2083.33 / (1 + 4.50 × 10^−3 * (140 - 20)) ≈ 234 ohms.

A Small Bulb Is Rated at 7