# [SOLVED]Vrms vs DC

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#### flyline19

##### Newbie level 5 When I convert from V (AC) to Vrms, Is that rms value similar to a DC equivlent? Im confused on what exactly rms tells me, like on a multimeter. When you measure, it tells you an rms reding, is that similar to a dc reading?

#### betwixt

##### Super Moderator
Staff member The RMS value produces the same power into a load as its numerically equivalent DC value.

However the two are not the same. Assuming we are talking about line (mains) electricity which has a sinusoidal waveform, RMS is used because the average value of a sine wave, taken over several cycles tends to zero which is obviously not a useful figure when calculating power. The conversion to RMS is a way around the measuring that gives a meaningful representation of the ever changing voltage as a static figure.

First the instantaneous voltage is squared, this removes the negative content of the waveform because squaring a negative value produces a positive in the same way as squaring a positive value would.

Then the average value over time is taken.

Finally, the square root of the result is taken. This reverses the initial squaring operation to re-scale the result.

Hence Root Mean Squared (RMS)

In a test meter this is rarely done although 'true RMS' meters are available that can handle any wave shape. Most DVMs simply rectify the AC into DC then scale the result to give the correct reading. It works perfectly well for sine shaped voltages but gives wrong results for any other shape.

Brian. The above have some interesting insight into RMS measurement. Especially the fact that many meters do not
measure properly an RMS value of waveform with a DC offset.

Regards, Dana.

#### KlausST

##### Super Moderator
Staff member When I convert from V (AC) to Vrms, Is that rms value similar to a DC equivlent? Im confused on what exactly rms tells me, like on a multimeter. When you measure, it tells you an rms reding, is that similar to a dc reading?

Why didn't you do an internet search?
Even Wikipedia tells:
"For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load."

Klaus

#### c_mitra When I convert from V (AC) to Vrms, Is that rms value similar to a DC equivlent? Im confused on what exactly rms tells me, like on a multimeter.

These concepts have deep mathematical significance. without going into details, let me elaborate the basic ideas.

1. Consider an arbitrary but otherwise periodic waveform. How to describe the waveform in terms of various properties.

2. The first parameter, the mean, is the arithmetic average. we define $\mu$ = $\int$f(t)dt (integral over complete cycles only)

3. The second moment, the RMS value, called variance in statistics, is the quantity defined as ${\mu}_{n}$ = $\int {t}^{n}f(t)dt$

4. We define third moment (skewness), the fourth moment (kurtosis) and all higher order moments are defined in the same way.

5. See, for a clearer picture, https://en.wikipedia.org/wiki/Moment_(mathematics)

6. Power is the second order term when the f(t) determines the voltage function. Hence the RMS value is related to the power (quadratic term).

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