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Multiple Choice
An incandescent lightbulb produces 100 W of light. If this lightbulb operates at 25% efficiency (meaning that out of all the power it generates, only 25% is released as light), what resistance must the lightbulb have if it operates at 120 V?
A
36 Ω
B
144 Ω
C
576 Ω
D
5.76 × 106 Ω
Verified step by step guidance
1
First, understand that the power output of the lightbulb is 100 W, but this is only 25% of the total power consumed by the bulb. To find the total power consumed, divide the light power by the efficiency: \( P_{total} = \frac{P_{light}}{efficiency} = \frac{100 \text{ W}}{0.25} \).
Calculate the total power consumed by the lightbulb using the formula from step 1.
Next, use Ohm's Law and the power formula to find the resistance. The formula for power in terms of voltage and resistance is \( P = \frac{V^2}{R} \). Rearrange this formula to solve for resistance: \( R = \frac{V^2}{P} \).
Substitute the total power consumed (calculated in step 2) and the given voltage (120 V) into the rearranged formula to find the resistance: \( R = \frac{(120 \text{ V})^2}{P_{total}} \).
Calculate the resistance using the values from the previous steps to determine which of the given options is correct.