Thermal Energy Dissipated in a Resistor in AC vs DC

In summary, to produce the same amount of thermal energy in a resistor, a direct current with a value equal to half the maximum value of an alternating current would need to be applied. Alternatively, one could integrate V*I*dt over a cycle or use the root mean square method to determine the equivalent DC current.
  • #1
Oijl
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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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  • #3


Yes, that is a correct approach. The average current in an AC circuit is given by the root mean square (RMS) value, which is half the amplitude for a sine wave. So, in this case, a DC current of 1.30 A would produce the same amount of thermal energy in the resistor as an AC current with a maximum value of 2.60 A. This is because the RMS value takes into account the varying nature of the AC current and gives an equivalent value that would produce the same heating effect in the resistor.
 

1. What is the difference between thermal energy dissipated in a resistor in AC and DC circuits?

In an AC circuit, the current and voltage are constantly changing in magnitude and direction, causing the electrons to constantly move back and forth. This results in a constantly changing resistance and therefore, a higher amount of thermal energy dissipated in the resistor. In a DC circuit, the current and voltage are constant, resulting in a lower amount of thermal energy dissipated in the resistor.

2. Why does thermal energy dissipated in a resistor change in AC and DC circuits?

The change in thermal energy dissipated is due to the nature of alternating and direct currents. In AC circuits, the constantly changing current and voltage leads to a constantly changing resistance and therefore, a higher amount of thermal energy dissipated. In DC circuits, the constant current and voltage lead to a constant resistance and therefore, a lower amount of thermal energy dissipated.

3. How does the frequency of the current affect the thermal energy dissipated in a resistor?

The frequency of the current in an AC circuit affects the thermal energy dissipated in a resistor in two ways. Firstly, a higher frequency means the current and voltage change more rapidly, resulting in a higher amount of thermal energy dissipated. Secondly, a higher frequency also means the electrons have less time to dissipate heat, resulting in a higher amount of thermal energy dissipated as well.

4. Are there any other factors that affect the thermal energy dissipated in a resistor besides the type of current?

Yes, there are other factors that can affect the thermal energy dissipated in a resistor, including the resistance of the resistor, the temperature of the surrounding environment, and the material of the resistor. A higher resistance or a higher temperature will result in a higher amount of thermal energy dissipated, while a different material may have a different thermal conductivity, affecting the dissipation of heat.

5. How can the thermal energy dissipated in a resistor be calculated in both AC and DC circuits?

In both AC and DC circuits, the thermal energy dissipated in a resistor can be calculated using the formula P = I^2 * R, where P is the power dissipated in watts, I is the current in amps, and R is the resistance in ohms. However, in AC circuits, the calculation may be more complex due to the constantly changing current and voltage, requiring the use of calculus and other mathematical techniques.

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