Thermal Energy Dissipated in a Resistor in AC vs DC

AI Thread Summary
To determine the direct current (DC) that produces the same thermal energy in a resistor as an alternating current (AC) with a maximum value of 2.60 A, it's essential to consider the nature of both currents. DC provides a constant thermal energy dissipation, while AC varies, requiring an average calculation. The average current in an AC circuit can be derived from its sine wave characteristics, leading to the conclusion that the equivalent DC would be the root mean square (RMS) value, not simply half the maximum value. Calculus can be used to integrate voltage and current over a cycle for precise calculations. Understanding these principles is crucial for accurately comparing thermal energy dissipation in AC and DC circuits.
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Homework Statement


What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?


Homework Equations





The Attempt at a Solution


A DC would dissipate a constant amount of thermal energy in a resistor. An AC would dissipate a varying amount, but oscillating, so there would be an average. Couldn't I just say that since I know that current in an AC circuit oscillates as a sine wave, that the "average current" would just be half the amplitude, and so that over a period of time that is a multiple of the period of oscillation, a DC of half of the maximum value of current for the AC would have dissipated the same amount of thermal energy as the AC?
 
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