Question

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?

   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?

Fundamentals of Physics

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 31, Problem 55

Instant Answer

Solved by Expert Sachin Rao

11/21/2020

Step 1

Step 1: The average power dissipated in a resistor when the circuit is AC or alternating is given by the formula: \[P_{avg} = I_{rms}^2 \cdot R\] where \(I_{rms}\) is the root mean square of the current and \(R\) is the resistance. Show more…

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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?

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Key Concepts

Root-Mean-Square (RMS) Value

The RMS value of an alternating current represents the equivalent direct current that would produce the same thermal energy in a resistor. Since power is proportional to the square of the current (I²R), using the RMS value accounts for the fact that the AC current varies with time. For a sinusoidal wave, the RMS value is calculated by dividing the peak (maximum) current by the square root of 2.

Power Dissipation in Resistors

In resistive circuits, the thermal energy produced due to an electric current is determined by multiplying the resistance by the square of the current (as stated by Joule's law). This relationship implies that when comparing AC and DC currents for the purpose of evaluating thermal energy production, the effective (or RMS) value of the AC current should be used since it directly relates to the power dissipated in the resistor.

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