Two different electrical devices have the same power...

Name: Problem 81, Chapter 20: College Physics for AP® Courses
Uploaded: 2019-10-08T10:34:33-08:00
Duration: 5 min 7 s
Channel: Manish Haldankar
Description: Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

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Key Concepts

Impact of Voltage Variation on Power Consumption

When the voltage applied to a device is changed while keeping its resistance constant, the power consumption does not increase linearly but rather with the square of the voltage change factor, as indicated by the P = V²/R relation. This quadratic relationship is key in understanding the significant effects that even small changes in voltage can have on power draw and current in electrical systems.

Electrical Power in Resistive Circuits

The electrical power consumed or dissipated in a resistive element can be expressed in several forms, most notably as P = V²/R and P = I²R. These equations highlight how power depends on voltage, current, and resistance, and they are crucial for determining the performance of electrical devices under various operating conditions.

Ohm's Law

Ohm's Law establishes the relationship between voltage, current, and resistance, stating that the voltage across a resistor is equal to the current through it multiplied by its resistance (V = IR). This fundamental principle is essential for understanding how electrical circuits operate and for analyzing the behavior of resistive loads when voltage or current changes.

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