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Real Power in AC Circuit Analysis
Math and Science
Concept of Real Power In this section, we will be discussing the concept of real power. Real power is the power that a load absorbs in a resistive network. We will first focus on instantaneous power and then move on to average power.
Instantaneous Power
Instantaneous power is the power at any given moment of time. It can be calculated by substituting the time t into the power equation. Although the equation may look complicated, it is important to understand it in order to discuss average power.
Average Power
Average power is calculated over a period of time. It is represented by the symbol P and can be determined by integrating the instantaneous power over the specified period. The phase angles in the equation are constants and do not change unless there are changes in the circuit components or frequency. By carefully examining the equation, we can see that some terms drop out when integrating over a period.
Calculation of Average Power
When calculating average power, the terms involving cosine and sine of the phase angle differences drop out because they integrate to zero over a period. Therefore, the average power is determined by the first term in the equation. The average power (P) can be expressed as:
P = Vm * Im * cos(θv - θi) / 2
Where Vm and Im are the maximum values of voltage and current, and θv and θi are the phase angle differences between voltage and current.
In this passage, we are discussing the concept of average power and how it relates to resistive networks. We first establish that when dealing with a constant term, the average of that term should be the same constant. This concept is important because it helps us understand how certain terms contribute to the overall average power.
Next, we visualize a resistive network and its current and voltage characteristics. We note that the current and voltage are in phase with each other, meaning they follow the same pattern. This information allows us to determine the instantaneous power, which is always positive for resistors since they cannot store energy.
Furthermore, we observe that the power has a doubling frequency compared to the voltage or current. This doubling frequency is a result of the trigonometric identities used to calculate the power function.
