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joel amos
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Why do we use the square of the graph as opposed to the absolute value of the graph to find the mean values?
The definition of electrical heat in a resistor is [itex]E=\int R\cdot I^{2}dt[/itex]. We want this expression to be the same for DC and AC. Since the AC waveform repeats itself after the period T, we want [itex]E=\int_{0}^{T} R\cdot I_{dc}^{2}dt=\int_{0}^{T}R\cdot I_{ac}^{2}dt [/itex]. Since R and Idc are constants, this is equivalent to [itex] R\cdot I_{dc}^{2}\cdot T= R\cdot\int_{0}^{T}I_{ac}^{2}dt[/itex]. After some reordering, we get [itex] I_{dc}^{2}= \frac{1}{T}\int_{0}^{T}I_{ac}^{2}dt[/itex].joel amos said:Why do we use the square of the graph as opposed to the absolute value of the graph to find the mean values?
RMS stands for Root Mean Square, and it is a mathematical method used to find the effective value of an alternating current or voltage signal. It is important in AC circuits because it represents the equivalent DC value of the signal, which is necessary for calculating power and determining the behavior of components in the circuit.
RMS is calculated by taking the square root of the mean of the squared values of the AC signal over one period. This accounts for the positive and negative values of the signal and results in a value that is equivalent to the DC value of the signal.
A square is used in the RMS calculation because it is the simplest shape that has an area, which is necessary for finding the mean value. Other shapes, such as triangles or sine waves, do not have a consistent area and would result in a more complex calculation.
Using RMS values in circuit analysis and design allows for easier calculations and more accurate results. It simplifies the process of finding power and understanding the behavior of components, making it easier to design efficient and effective circuits.
In some cases, using RMS values may not be necessary, such as in simple circuits with only resistive components. However, in more complex circuits with reactive components, using RMS values is essential for accurate analysis and design.