RMS in AC circuits

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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?
 

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Svein
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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].
So - the equivalent DC current of an AC current is the square Root of the Mean of the Squares.
 
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