# Difference between Vdc and Vrms

#### Mishaerachae

##### New Member
Anyone to help me distinguish between Vdc and Vrms confused.

#### Mishaerachae

##### New Member
I am a second year electrical Engineering student and so far I have been picked up that Vrms is the component of a rectified ac signal that will deliver the same power as dc. But now I am told that Vdc = 0.318Vm and Vrms =0.707 which is not the same. Confused.

#### Nigel Goodwin

##### Super Moderator
so far I have been picked up that Vrms is the component of a rectified ac signal
Well you've 'picked up' wrong, Vrms has nothing to do with a rectified signal - and I find the answer in post #2 a little confusing?.

The 'classic' explanation of RMS is that it gives the same heating effect as the same DC voltage.

I've no idea what Vm is even supposed to mean? (and neither does google), but 1V DC equals 1 V RMS.

Simple example:

Mains in the UK is 240V AC RMS, if you connect a 3000W heater to it, you get 3000W of heat out of it - if you connect a 240V DC supply to the same heater, you get the exact same 3000W of heat out.

#### Mishaerachae

##### New Member
Please tell me more. My main source of confusion is exactly that. Please explain why Vdc and Vrms have different values. Vm stands for Vmax or Vpeak

#### dknguyen

##### Well-Known Member
Please tell me more. My main source of confusion is exactly that. Please explain why Vdc and Vrms have different values. Vm stands for Vmax or Vpeak
This question doesn't make sense. I think you are mistaking the average voltage for DC. The average value of a HALF-rectified waveform is 0.318*Vpeak. The average of a full rectified wave is 0.637. The average value of a rectified wave is not the same as DC.

Obviously, for DC, DC = avg = rms but this is not true for waves because the squared part of I^2*R or V*2/R make dissipate disproportionately more power at the peaks and disproportionately less power near the valleys.

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#### Nigel Goodwin

##### Super Moderator
Please tell me more. My main source of confusion is exactly that. Please explain why Vdc and Vrms have different values. Vm stands for Vmax or Vpeak
Well you can't compare peak with RMS, there's no relationship between them. And Vdc and Vrms don't have different values, that's the whole point of RMS. I fail to see how you can even say "Vdc = 0.318Vm", where Vdc is a DC voltage, and Vm is the peak of an AC one?. Who made up Vm?, and why?.

#### audioguru

##### Well-Known Member
Many poor quality audio amplifiers say peak power instead of RMS power to make the number larger. 100W Peak = 50W RMS.
50W RMS is produced by 20V RMS in 8 ohms. For a sinewave, the peak of 20V RMS is 28.28V. 100W Peak also has a peak voltage of 28.28V, and an RMS number of 20V.

#### Prototype

##### New Member
Nigel Goodwin I think said it best, although I disagree with his statement
Well you can't compare peak with RMS, there's no relationship between them
The rms value of a sine wave is 0.707 x the peak value, that is the relationship.

#### audioguru

##### Well-Known Member
But many waveforms are not a sinewave. Narrow pulses (drum beats?) have a high peak voltage but a low RMS voltage.

#### MichaelaJoy

##### Active Member
RMS means "root mean square". That's where the .707 comes from, with regard to a sine wave.

$\sin(\pi/4)\;=\;1\;/\;\sqrt2$

#### Prototype

##### New Member
But many waveforms are not a sinewave. Narrow pulses (drum beats?) have a high peak voltage but a low RMS voltage.
True, but the maths starts to get a bit too complicated for me if its any more than a sine wave or a square wave

#### Ratchit

##### Well-Known Member
I am a second year electrical Engineering student and so far I have been picked up that Vrms is the component of a rectified ac signal that will deliver the same power as dc. But now I am told that Vdc = 0.318Vm and Vrms =0.707 which is not the same. Confused.
You had better get a good understanding of RMS, or you are in for a rough, tough ride in the electrical field.

RMS is the equivalency factor with respect to the power. For instance, you cannot expect a sine wave to output the same average power that a constant amplitude voltage/current does when both have the same peak value. In fact, a 1 volt peak sine wave outputs only 70.7% of the power a 1 volt constant amplitude source would produce. That is because the sine wave dips down to zero twice during each period.

To figure the root-mean-square (RMS), take the square of the wave value of every instant of time during an appropriate period. Next, find the average of the squares. Then take the square root of that average. Below are some sample calculations for a sine wave. The square is necessary because power is proportional to the square of voltage/current.

An average responding meter only measures full sinusoidal waves accurately. For other waveforms, use a true-RMS meter which calculates the RMS value like I did above.

Ratch

#### NsrMagazin

##### Member
320VAC peak to peak = 230VAC RMS -> Rectifier ->230 impulse DC with the losses -> capacitor -> almost fully flat line DC.
There is no VDC RMS. Thats a bit different.

VAC peak to peak /square root of 2 = VAC RMS

We divide by the square root of 2 to get VAC RMS so we can use the same formulas as we use for DC.

#### Nigel Goodwin

##### Super Moderator
Nigel Goodwin I think said it best, although I disagree with his statement

The rms value of a sine wave is 0.707 x the peak value, that is the relationship.
Except no one specified sinewaves, as I said there's no relationship between peak and RMS, other than for exact individual ones - it doesn't need to be a sinewave, in can be any wave as long as it never changes, but each wave will have a different relationship.

#### JimB

##### Super Moderator
320VAC peak to peak = 230VAC RMS
A couple of errors in that statement:
It should say
325 V PEAK = 230 V RMS

Similarly the statement:
VAC peak to peak /square root of 2 = VAC RMS
Should say
VAC peak /square root of 2 = VAC RMS

Peak to peak is twice the value of peak.
All this applies to a sine wave.
If the waveform is not a sinewave, all bets are off.

JImB

#### Nigel Goodwin

##### Super Moderator
A couple of errors in that statement:
It should say
325 V PEAK = 230 V RMS
I find it quite annoying that people use 230V in examples, as no one uses that for their mains voltage

#### kubeek

##### Well-Known Member
I find it quite annoying that people use 230V in examples, as no one uses that for their mains voltage
Why do you think so? All europe uses this voltage. (I don´t count UK, since it is very soon to be somewhere in the middle of the atlantic )