# RMS in AC circuits

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 $E=\int R\cdot I^{2}dt$. We want this expression to be the same for DC and AC. Since the AC waveform repeats itself after the period T, we want $E=\int_{0}^{T} R\cdot I_{dc}^{2}dt=\int_{0}^{T}R\cdot I_{ac}^{2}dt$. Since R and Idc are constants, this is equivalent to $R\cdot I_{dc}^{2}\cdot T= R\cdot\int_{0}^{T}I_{ac}^{2}dt$. After some reordering, we get $I_{dc}^{2}= \frac{1}{T}\int_{0}^{T}I_{ac}^{2}dt$.