What is the operating resistance of a 30-watt light bulb designed for a 28-volt system?

• A. 26 ohms
• B. 28 ohms
• C. 30 ohms
• D. 22 ohms

Answer: (A)

To find the operating resistance, use R = V^2 / P with the rated voltage and power. For a 28-volt bulb designed for 30 watts, R = 28^2 / 30 = 784 / 30 ≈ 26.1 ohms. So the operating (hot) resistance is about 26 ohms. The filament’s resistance is higher when hot than when cold, which is why we use the rated operating values rather than the cold resistance. If the resistance were 28 ohms, the power at 28 V would be 28^2 / 28 = 28 W, and at 22 ohms it would be about 35.6 W, which wouldn’t match the rated 30 W.