What is the operating resistance of a 50-watt light bulb designed for a 14-volt system?

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BlackTom AI · Accepted Answer

Question restatement: What is the operating resistance of a 50-watt light bulb designed for a 14-volt system?

Answer options provided: ["4 Ohms"]

Analysis of the option:
- Start with the fundamental relation for DC electrical power: P = V^2 / R, which can be rearranged to R = V^2 / P.
- Here, the operating voltage V is 14 V and the power P is 50 W. Plugging in these values gives R = 14^2 / 50 = 196 / 50 = 3.92 ohms.
- The operating resistance of a filament bulb is determined at its operating temperature, where the filament resistance is higher than at ambient temperature due to temperature-dependent resistivity. The calculated 3.92 ohms reflects the resistance at operating conditions, which is typically rounded in common practice.
- Therefore, 3.92 ohms is essentially the same ballpark as 4 ohms, and designers or specifications often quote approximately 4 ohms for practicality and rounding.

Notes on the single option:
- Since only one option is presented, there are no alternative choices to evaluate for correctness or incorrectness. If there were other options, we would compare their values to the calculated 3.92 ohms and discuss discrepancies due to rounding, temperature effects, or measurement conditions.

Overall takeaway: Using R = V^2 / P with V = 14 V and P = 50 W yields approximately 3.92 ohms, which aligns with the provided option of 4 Ohms when rounded to a convenient value.

AMT&101 36393 Test - Basic Electricity

What is the operating resistance of a 50-watt light bulb designed for a 14-volt system?

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