Hi!
I'm currently taking a class called AC Principles and have a few questions. Our instructor has been teaching us about sign waves and I'm having a hard time understanding peak voltage.
How do we know that the peak voltage of a 120VAC sign wave comes to 170 volts?
And how does the figure ".707" relate to the 170 volts?
We'll be getting into 3-phase in the next class and I don't think I have grasped this concept yet.
Thanks!
Peak Voltage:
Peak voltage tell you how far the voltage swings, either positive or negative, from the point of reference. Peak voltage is only a moderately useful way of measuring voltage when trying to express the amount of work that will be done when driving a specified load.
RMS Voltage:
RMS voltage is absolutely the most common way to measure/quantify AC voltage. It is also the most useful. Because AC voltage is constantly changing and is at or near the highest and lowest points in the cycle for only a tiny fraction of the cycle, the peak voltage is not a good way to determine how much work can be done by an AC power source.
The RMS voltage of a pure‡ sine wave is approximately .707*peak voltage. If you read voltage with a voltmeter you are generally given the RMS voltage of the wave form.
So for your example the sine wave goes from 0 to 170V in the positive and then goes down to 170V in the negative. To find RMS (peak Voltage) x (0.707) this will give you 120V.
If you hooked up an osiliscope to a 120volt receptacle you would see the sinewave and would notice that the highest voltage that is recorded is 170volts. This is Peak Voltage. Its only there for a really, really short time. So use the RMS (RMS is .707 of Peak Voltage)
[This message has been edited by RobbieD (edited 01-29-2006).]
Thank you for that explanation. I really do appreciate the help. So if I know 170 volts is the peak voltage level for a 120 volt sine wave, would I also use the .707 figure to find the peak level of a 24OV sine wave? How 'bout 480?
Yes. The .707 is a constant. If you read 240Volts with your multimeter you are reading RMS Voltage. So the peak voltage would be 240/0.707 so Vp=340
If Vrms=480 480/0.707 so Vp=679
This is true for a sine wave, not necessarily for other wave shapes. It has to do with the square root of 2, a bit of trig trickery (not unlike smoke & mirrors).
Hook up a scope to an AC circuit and see the peak values are + & - 170V. Then divide 170 by the square root of 2 (1.4142) and you get 120V (approximately) RMS value. RMS is the effective, or DC equilivant value, work wise.
Radar
The RMS value of a sine wave voltage generates the same amount heat for a resistor at the same DC value.
e.g. 120 VoltsRMS AC generates the same amount of heat as 120 Vdc, regardles of the higher peak value. ( and lower values near the zero crossing )
Robbie gives you a very good explanation for it anyway.
In case of 3Ø power the value V3 or root 3 (1.73) becomes more important as you will learn at tech. later on.
Phase voltage between phase and neutral. is 120 volts in your case.
Line voltage is 120*1.73=208 volts, between 2 phases.
Hope it helps a little
regards Ray.
The .707 is the square root of the integral from 0 to 2π of sin(θ)^2 dθ, divided by 2π. Which is, as RobbieD said, the RMS value of the waveform. That integral comes out to 1/sqrt(2), which is, rounded to three digits, 0.707.
(Edited to turn off smilies, which were showing up in the middle of the math.)
[This message has been edited by SolarPowered (edited 01-30-2006).]
I love this forum!
Thanks to all of you.
Really.
Ron