RMS Value of AC Circuits
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- Опубліковано 30 вер 2024
- This electronics video tutorial explains how to determine the RMS value of AC circuits. It explains how to calculate the root mean square or rms voltage of a sine wave given the peak voltage. It also provides the process that can help you derive the formula using basic math and calculus.
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I have a better way to understand this. The RMS value is the value we get, when we are half way up to our peak. If the voltage was increasing linearly, a straight line, then the halfway point is 0.5 time peak voltage.
But the voltage is increasing in a perfect circle. The circle starts at zero degrees, at 90 degrees we are at peak, 180 back to zero, 270 peak bottom and 360 back to zero. so, halfway from the first peak is 45 degree of a circle. To get the voltage at the halfway (remember your high school trigonometry) you need to do Sin(45) = 0.707. Thats it!
so sin(0) = 0 volts, starting voltage.
Sin(45) = 0.707, halfway peak
Sin(90) = 1, peak voltage
sin(135) = 0.707, halfway down
sin(180) = 0. a half circle complete. now we do the bottom half
sin(225) = -0.707, halfway to peak, but negative value this time!!
sin(270) = -1 peak bottom voltage
Sin(315) = -0.707, halfway back up
Sin(360) = 0, full circle complete.
So, basic trigonometry, if you know circles and basic sin law. the average is, the midway point from zero to a peak, or 0.707*peak value. You don't need to do all the math he did, just sin(45). it is intuitive if you understand 90 degree is from nothing to peak, 180 back to zero and so on. So 45 degrees is midway average = 0.707
Q find the avarag output currant and its root mean square RMSof output current ? ممكن تساعدني بالحل باسرع وقت
So, you have a point. But, on Electrical exams they dont let you use a calc that has the (sin) button, basic calculators only. Therefor it is necessary to know to do the hard math.
He did not do all the math to get this result, he did the additional steps to prove the rms value.
If you know the 2 special triangles and trig you can figure this out. I used this to solve for rms. 0.707 is what they ask for in class but I like using sin45, which is root 2/ 2. This might not be technically the exact number to Express the equivalent amount of heat from ac current to a DC equivalent, but root 2/2 is very close, and .707 is good enough to get an idea of your voltage. In other words, trig is enough to work this out. I don't know why is school they said using sin 45 was incorrect and .707 was correct. Someone can help me with that.
Thank you dude, I knew there was a geometric explanation to convert the sine wave into an equivalent linear value but you cleared it up for me. Cheers mate
Bro are you one of my classmates? Your video releases almost always align with what I’m currently learning in class. Like we literally did rms values today.
No he's not in special Ed classes I don't think
@@giziemcbarns lol
😂
Dude he joined in 2015, and he has published a book. I don't think he goes to college/high school anymore lol
@@giziemcbarns Shots fired 💀
You immediately state that Vpk = √2 Vrms. However, you have jumped too far ahead already. WHY do you use √2? It doesn’t do anyone any good just to tell them to use a √2 unless you explain the significance of where and why there is a need to use a square root. Without explaining why the √2 just magically appears, you are just reciting a formula for people to copy and calculate, yet you have dropped the fundamental explanation of WHY the square root came to be used in the first place. Please provide an explanation to tell the viewer why every single variable exists in the equation. Don’t assume people understand what the function of the √2 is, where it came from, and why it is so significant in this equation. Thanks
I searched on Google for this, since I have to calculate the peak voltage of my 240 VAC line , but I took calculus in 1971, over 53 years ago and I did not remember how to calculate RMS and peak. Your explanation is very clear! Thank you!
So glad you have this UA-cam channel. It changed my life
Man I hope you know that without you I would've failed basically everything. U the goat fr!
While the final value is correct owing to the symmetry of sin²(t), the concept of RMS value should have been calculated with integral limits should have been 0 to the period of the waveform [in the case of sin(t) should be 0 to 2π..]. Otherwise you'd quickly run into trouble with non symmetrical waveforms, such as any square waveforms with anything other than 50% duty cycle.
Simpler way to unerstand this for sine AC is to take the sine func, square it and than root it so its always positive, then take median value of the amplitude which is sin45, or the √2/2 as a coefficient, and then multiply the peak with it to average it out. Not sure about mathematical validity of this, but it makes practical sense.
I correlated the value to multiply the peak voltage as being very close to sin(pi/2). So I decided to use square root of 2 divided by 2 in my rms calculations. My instructor said I was wrong, and that I should use 0.707 instead. So I use .707 in his class and square root of 2 divided by 2 outside of his class. I'm happy someone covered this! Rather than just saying so use .707 without explanation.
Hi the rms voltage is not the same precision that a true rms multimeter , example, my multimeter give me 5.7 vrms and my scope 5.3 vrms on my amplifier
@The Organic Chemistry Tutor what is the program you are writing on?
Why don’t we just use the mean of the absolute value of the sin idk ig I’m dumb
شرح مثالي🙆♀️🌹
God bless you man , you have helped me and us of course.
Hi, do you have any videos dealing with economics equations?
So nice my best teacher who made me understand logic gates u are the best 100%
Great explanation. Mark Walberg, is this you? :D
its julio g.
Excellent explanation. However, there is nothing special about Vrms - it is just an estimate of the non-peak voltage over a cycle. Vrms is used because, by convention, people have chosen the rms value as the estimate to cite. RMS (root-mean-square) is the first go-to in statistics when the average fails (i.e., equals zero, as it does in your example).
Anyone can see rms=peak*1.4 is not the same as rms=(peak*1.4)/2…. Maybe I missed something but it’s literally just chopped in half.
Thanks for the video! I was taught RMS, but was never actually taught what it was. It doesn't help that books and teachers use "RMS" and "average" interchangeably, even though they aren't the same (average value of sinusoidal is 0). Thanks for the explanation!
Anderson Angela Jones Robert Rodriguez Ronald
Please I need help for the period part
Isn't the formula for V= Vm(sinwt)? Where w= 2π/T, are we using the period as 2π or just π?
in my own view, w= 2π/T it's help you to calculate the Hz but almost in period that mean 1 compleat cycle of the AC so if set the π is compleat period just use the π
Thank you for great explanation, but you made a small mistake at the end of the video. The upper bound of the integral and denominator should be 2pi.
Or just do the peak value (volt)/ by √2☺️....1/√2 = 0.7071
Isn't it 1/T? And the quotient is t/T?
Hi do you have tutorial on calculate rms using triangular waveform?
It was great explanation, I would like to know what will be the result if we consider negative cycle of the supply. And would also like to ask is this rms value remain same for the whole positive cycle with equivalent to ac supply as you have mention in the begining of the video.
Excellent and Thanks 🙏👍👌💯
Thanks អរគុណ❤
Where does the sqrt(2) come from, can someone explain please.
Very detailed explanation. Thank you very much.
Can you make video about harvesting circuit
I understand *that* RMS yields the equivalent DC voltage, I just don't get why mean doesn't. I would expect that taking the arithmetic mean of 1/2 cycle would yield the correct result, but it doesn't. I don't understand why that is.
I believe that all one is trying to do is get an estimate of the non peak voltage. There is no "correct result" - just an estimate. This is a standard problem in general statistics. By convention people have chosen that estimate to be the root-mean-square voltage, Vrms = .707*Vpeak = 30V in his example. If we chose your definition as the estimate we would get
Vest = (2/Pi)*Vpeak = 27V. This voltage is a perfectly good estimate - just not the conventional estimate. In science and engineering it is important to stick to a convention so that we can communicate with one another with clarity.
Kayleigh Dam
Ur videos are very helpful, thx
Why a sine wave instead of cosine wave? Also overall a thorough explanation of what root mean square expresses really! 💯
Sine wave and cosine wave are the same, only phase shifted by 90 degrees. So it applies for either.
@@Ecelleon thank you!
Great explanation
Sawayn Parkways
Roscoe Estates
Thank អរគុណ
Organic chemist teaches electronics.. Whats wrong?
He teaches almost everything
Hey man, long shot you'll see this, but why is 1/t 1/pi? I'm under the impression that t is the period, which for a sin wave is 2pi right?
We are only looking at the positive half of the cycle.
@@tj595555 awesome, thanks
The positive half is symmetrical to the negative half. Imagine flipping the negative half over the line to the positive side then cutting of the tops of the peaks to fill in the valleys. This is essentially the idea of vrms's effect. Leveling out the fluctuating voltage value to see what the overall effect is in terms to express it like a DC circuit. At least that's my perspective. Take it with a grain of salt and your own research.
Current in a resistor is a start-stop motion of conduction band electrons due to their collision with the rocking lattice ions, and this causes a resistor with a sinusoidal voltage applied, to produce heat. The polarity reversals of an applied sinusoidal voltage (with the direction reversals of the applied electric field) do not affect electron collisions with the lattice ions. Electrons colliding with lattice ions from either direction will continue to produce heat and there is no cancellation of the heat developed!
Mathematically, the average value of a sinusoid is zero, and so, the average value of the current will also be zero. The average values cannot therefore represent the heat developed in a resistor with a sinusoidal current.
A resistor cannot develop heat due to a current in one half-cycle and then cool itself by a like amount of heat during the next half-cycle! It develops heat either way whether the current is positive or negative. The lattice ions vibrate from collisions irrespective of the directions in which the electrons collide with them. Therefore, since the average value is zero, it necessitates the use of the root-mean-square values of the voltage and current to compute the power, which is a statistical measure of the magnitude of a varying quantity and is the square root of the arithmetic mean of the square of the sinusoidal function.
Electrostatics and circuits belong to one science not two. To learn the operation of circuits it is instructive to understand Current, the conduction process, resistors and Voltage at the fundamental level as in the following two videos:
i. ua-cam.com/video/TTtt28b1dYo/v-deo.html and
ii. ua-cam.com/video/8BQM_xw2Rfo/v-deo.html
It is not possible in this post to discuss in more detail average and rms values.
The last frame References in video #1 lists textbook 4 which discusses in detail using a unified approach sinusoidal voltage, current, their average and root mean square values.
SIr,
why only till "pi' why not "2pi??10:35
We are only looking at the positive half of the cycle, so we are only looking at half of a revolution.
thanks a lot
Thanks so much for your videos.
I subscribed
Why v(t)=sin(t)
XD
smooth explaination... :)
Thank you
Hi , I like your video
Awesome
thank you
🔥🔥🔥🔥
Thank you Sir, some "Profs" are lacking the ability to tell RMS integration is valid for all waves and not just sinus waves.
First to comment 😎
congrats
You will never get past reading WIKI pages. What a waste.
What?
@@arthurmead5341 🤣
this guy must be a professor