When do we use rms value or mean value in calculations? What are their physical significance, if any?
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/41779/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Apr 12, 2018 at 13:10
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There is no physical significance as such other than the fact that it allows for a better way to describe data mathematically.
Imagine an AC current, constantly oscillating.
- $\mathrm{mean(...)}$: What is the mean value here? It is zero. That is a useless measure.
- $\mathrm{max(...)}$: We could instead simply use the maximum; the top of the current peaks. That is not a useless measure, although it says nothing about the width of these spikes.
- $\mathrm{mean(abs(...))}$: If we really want some kind of "averaging" that represents the widths and height and thus overall pattern then we could maybe first flip all negative values to positive before finding the mean (that would be the mean of the absolute values). This would give an average value not at zero but close to the zero-line, since the large "bottoms" of the spikes will weigh heavily on the mean.
- $\mathrm{rms(...)}$: If we want the peaks to weigh more than the "bottoms", then the RMS value may be appropriate. The RMS or root-mean-square value is first squaring the values, then taking the mean and then neutralizing the squaring by taking the square root: $$\mathrm{RMS}=\sqrt{\frac{x_1^2+x_2^2+x_3^2+\cdots}n}$$ Squaring a large value has much more impact than squaring a smaller value, so in the RMS value, the peaks will weigh much heavier than the bottoms and the RMS value is somewhere higher up nearer to the peak tops.
See more in this other answer: Why do we use Root Mean Square (RMS) values when talking about AC voltage
