Will Matney wrote:
>I've been setting back and watching this and hope some aren't confusing rms
>and average voltage as the same thing.
>
The confusion seems to be more about average power and RMS power.
>RMS or (root mean square) is calculated as 0.707 X peak voltage. The average
>voltage is calculated by 0.637 X peak voltage. This is the way I was taught
>and is in several of my books here which I already have double checked myself.
>
The average voltage of a sine wave is 0.
>One can be fooled but rms and average are not the same.
>
Some of us know that. Some don't seem able to appreciate it. The top of
this page
http://www.g8wrb.org/useful-stuff/rmspower.html
has the formula for RMS and the formula for mean.
Those formula assume nothing about the waveform at all, other than it is
periodic. But it can be sine, square, triangle or whatever else you want
to come up with. As long as it is periodic, the two formula at the top
will give you the RMS and mean respectively. They work for voltages,
currents, noise from a ticking clock .... anything that is periodic,
with a period of T. For sine waves, the period T is 360 degrees (2 Pi
radians).
>This can be confused when talking about meter movements and them being
>designed to read avarage or rms values (some average reading calibrated to
>read rms).
>
All of the common meters (AVO, moving coil and cheap DVMs) are
calibrated assuming a sine wave. If the waveform is not sinusoidal, they
read incorrectly. Some of the better DVM's can read true RMS.
>Quoted from the "Modern Dictionary of Electronics";
>
Sorry to say, I'm not over-impressed with this - see below.
>"Average value: The value obtained by dividing the sum of a number of
>quantities by the number of quantities.
>
That only applies to discrete quantities, like apples, pears etc. It
does not apply to a continuous function like a sine wave.
>The average value of a sine wave is 0.637 times the peak value".
>
Well that is just silly. The average of a sine wave is 0.
>"Average voltage: The sum of the instantaneous voltages in a half cycle
>waveshape, divided by the number of instantaneous voltages. In a sine wave,
>the average voltage is equal to 0.637 times the peak voltage"
>
Well they define an average value, now for a sine wave bring in this
extra thing about half a cycle!!! Why should the average voltage be any
different from the average of anything else? An average is an average.
The average of a sine wave is 0, as it is mathematically correct to do
the averaging over a complete cycle - not half a cycle. However, doing
it over a complete cycle will give zero.
It seems they are computing the average of a full-wave rectified sine
wave, not a sine wave. That repeats every 180 degrees, or Pi radians.
Using my old friend Mathematica, which makes these sorts of calculations
quite easy,
In[4]:= 1/( Pi) *Integrate[ Sin[t], {t, 0, Pi}]
2
Out[4]= --
Pi
which is indeed approximately 0.637, if we take the numerical value of it.
In[5]:= N[%]
Out[5]= 0.63662
So I can see how they arrive at 0.637, but to me it is not the average
of the sine wave. It's the average value of a full wave rectified sine
wave - assuming the bridge is perfect.
>The ac rms value is known as the "effective value" or the same value that
>would produce the same work as a DC value.;
>
AC RMS value of what - voltage, power, energy, charge ..... what do
they mean???
>"Rms voltage: The effective value of a varying or alternating voltage. That
>value which would produce the same power loss as if a continuous voltage were
>applied to a pure resistance. In sine wave voltages, the rms voltage is equal
>to 0.707 times the peak voltage".
>
So they have defined the effective voltage as being the RMS voltage, and
the effective current as being the RMS current. They have *not* defined
an effective power.
>"Watt: A unit of the electric power required to do work at the rate of 1 joule
>per second. It is the power expended when 1 ampere of direct current flows
>through a resistance of 1 ohm. In an alternating current circuit, the true
>power in watts is effective volt amperes multiplied by the circuit power
>factor".
>
Yep,
P = V I cos(phi)
where P is the mean power
V is the RMS voltage
I is the RMS current
phi is the phase angle between the voltage and current.
Note now they say the "the true power in watts...". They have not
defined true, but I take that as meaning mean. If you interpret 'true'
as 'mean' then they are right.
>The above explains the use of two wattage formulas. Notice it says the watts
>in an ac circuit are the "effective" volt amperes which means the rms value,
>not average.
>
Yes, and I don't think anyone is arguing about that. To say the average
value of voltage would be silly, since the average is 0 anyway.
Rich agrees
Power = Vrms * Irms,
it is just that he thinks the power is RMS power, where myself and
others think it is mean power.
>Hope this helps reveal things through all the smoke.
>
You will be so lucky!!
--
Dr. David Kirkby,
G8WRB
Please check out http://www.g8wrb.org/
of if you live in Essex http://www.southminster-branch-line.org.uk/
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