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

Question

BlackTom AI · Accepted Answer

To determine the operating resistance of a lamp, use the basic relation R = V^2 / P.
Option 1: 4 Ohms. Using V = 14 V and P = 50 W, R = 14^2 / 50 = 196 / 50 = 3.92 ohms, which is effectively 4 ohms when rounded for practical resistor-like behavior in a bulb. This aligns with the expected, near-4-ohm resistance at operating power.
Option 2: 3 Amps. While current can be found from I = P / V = 50 W / 14 V ≈ 3.57 A, this is not a resistance value. The question asks for resistance, not current, so this option confuses current with resistance.
Option 3: 14 Ohms. If the resistance were 14 ohms, the current would be I = V / R = 14 V / 14 Ω = 1 A, and the power would be P = V^2 / R = 14^2 / 14 = 14 W, which does not match the given 50 W. This demonstrates a mismatch between the stated power, voltage, and resistance.
In summary, the correct way to assess the operating resistance is to apply R = V^2 / P using the given voltage and power, which yields a value very close to 4 ohms. The other options either mix up current with resistance or produce inconsistent power calculations for the given voltage.

AMT102 36396 Test - BE Practical Apps

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

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