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Ch. 25 - Electric Current and Resistance
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 25 - Electric Current and ResistanceProblema 35
Capitolo 24, Problema 35

You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.]

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Determine the resistance of the 75-W lightbulb when it operates at 240 V. Use the formula for power: P = V2 / R, where P is power, V is voltage, and R is resistance. Rearrange to solve for resistance: R = V2 / P.
Substitute the given values for the European operation: V = 240 \(\text{ V}\) and P = 75 \(\text{ W}\). This will give the resistance of the bulb, which remains constant regardless of the voltage.
Now calculate the power consumed by the bulb when it operates in the United States at 120 V. Use the same power formula: P = V2 / R. Substitute V = 120 \(\text{ V}\) and the resistance R calculated in the previous step.
Compare the power consumed by the bulb at 120 V to the power of a standard 75-W 120-V bulb. The brightness is proportional to the power consumed, so the ratio of the two powers will give the relative brightness.
Express the relative brightness as a fraction or percentage by dividing the power consumed by the bulb at 120 V by 75 W (the power of the standard bulb) and multiplying by 100 if needed.

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Power and Brightness

In electrical systems, power (measured in watts) is the rate at which energy is consumed or converted. For lightbulbs, brightness is often proportional to the power they consume; thus, a bulb rated at 75 W will generally be brighter than one rated at a lower wattage. Understanding this relationship is crucial for comparing the brightness of bulbs operating at different voltages.
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Power

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor, expressed as V = IR. This principle helps in determining how the current changes when the voltage is altered, which is essential for analyzing the performance of the lightbulb at different voltages.
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Resistance and Ohm's Law

Resistance and Voltage Relationship

The resistance of a lightbulb remains constant when its temperature is stable. When using a bulb designed for 240 V in a 120 V system, the power consumed can be calculated using the formula P = V^2/R. This means that at a lower voltage, the power (and thus brightness) will decrease, which is key to understanding how the bulb will perform in the U.S. compared to its intended use in Europe.
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RMS Current and Voltage
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