02 - Sinusoidal AC Voltage Sources in Circuits, Part 1
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- เผยแพร่เมื่อ 4 มิ.ย. 2024
- View more lessons from this course at www.MathTutorDVD.com.
In this lesson, you will learn how to write sinusoidal voltage sources in AC circuit analysis. We will discuss the amplitude of the source, its frequency, and its phase angle to write the time domain sinusoidal voltage equation.
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I came to just learn about the phase angle but your explanation of the angular frequency gave me a much better understanding of the equation as a whole. Many thanks!
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A sinewave depicts movements in the form of waves. It has a datum, rapid, slowing and steady growth in one direction for a quarter cycle with reference to a datum (a reference), and then slow and faster decay in one direction for the next quarter cycle, and all these elements again in the opposite direction (reversal) of the forward movement for the next half-cycle. It has peaks and valleys.
In essence, the sinewave is a perfect embodiment of oscillatory movements like springs and quantities like voltage. It retains its waveshape when added to another sinewave of the same frequency and arbitrary phase and is the only periodic waveform which has this property.
The charges in a resistor subject to a sinusoidal voltage do not migrate elsewhere on the average. They merely slosh back and forth, so to say, over each cycle without a change in their position when the resistor was not energised.
Electrostatics and circuits belong to one science not two. To learn the operation of circuits it is instructive to understand Current, the conduction process and Voltage at the fundamental level as in the following two videos:
i. th-cam.com/video/TTtt28b1dYo/w-d-xo.html and
ii. th-cam.com/video/8BQM_xw2Rfo/w-d-xo.html
A sinusoidal voltage generator operates by separating charges for the positive half-cycle in one direction initially rapidly and slowing down and momentarily halting when its voltage is at the positive peak, and then gradually reuniting the separated charges to make the separation zero; when all charges reunite, the generator voltage is zero. The negative half-cycle now commences, when the generator operates by separating
charges in the opposite direction initially rapidly and slowing down and momentarily halting when its voltage is at the negative peak, and then gradually reuniting the charges to make their separation zero; when all charges reunite, the generator voltage is zero. It then begins the next positive half-cycle followed by the negative half-cycle and the process repeats.
The last frame References in video #1 lists textbook 4 which discusses these topics in more detail using a unified approach and provides an intuitive understanding of sinusoidal steady-state voltages and currents in capacitive and inductive circuits.
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I have a question about the derivation of the instanteous power - specifically when the current phase is shifted by thetaI. If I went to phasor land and multipled the original volts (120cost(wt+thetaV)) time amps (120cost(wt+thetaI)) I would get V*I@angle(thetaV+thetaI). After doing the phase shift according to the demonstrated calculation (and the formal published power formula) I am now at (thetaV MINUS thetaI). How do I reconcile this mathematically?
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Another question on the same issue. How do i calculate time?
Q: A 50Hz sinusoidal voltage has an rms value of 200v. The initial instantaneous voltage is zero and rising positively. Find the TIME taken for the voltage to reach a value of 141.4 V for the first time.
Please help with this also. I just need step by step examples.
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Sir in sinusoidal I think the eqn should be in sine but you have used cosine why sir can you clarify??
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What is the independent phase of sinousidal voltage?? Tell me
Amazing: Fast but not too fast, coherent, easy to understand 10/10
Is there any specific reason to use cos function in voltage and current equation, why usually all books shows these equations in cos function rather than sine.
No good reason. Cos and sin are exactly the same and only differ by a phase shift. I think using cos is just for historical reasons.
Sir, Why did you use v=Vcos(theta) instead of v=Vsin(theta). I've seen both online. You quickly said "we could use either one". How is that possible?
Wouldn't you need to be told the Voltage @ time =0 in order to calculate the instantaneous voltage after a given time period?
You can use either of them as long as you take into account the 90 degree phase difference between the two signals
Is angular frequency the same as angular velocity?
grt lecture but wish other lectures to be free
You should send them to a sin curve explanation so that they would understand this relationship. A sine or cosine curve is based on a circle, which has 360 degrees or 2PI to go around once (the period). So the normal PERIOD of a sine curve (or cosine curve it follows the same rule, cosine curves are just sine curves 90 degrees out of phase, more functions study required) y=sin(x) is 2PI. As an example the period in this equation y=sin(2x) would be controlled by that 2, and oddly enough that 2 DOES NOT double the period, it halves it (more functions study required), so curve y=cos(2x) is 180 degrees. If I wrote y=sin(1/2 x), I would do the inverse, DOUBLE my period to 720 degrees. If I WANT TO GET rid of the 360 period ENTIRELY to work in lets say seconds, and turn it into a period of 1, I would write this: y=sin(2PIx). I'm actually dividing (NOT MULTIPLYING) the period by 2pi to bring it down to a period of 1 (2pi/2pi =1)). By making the OMEGA =2PIf, you are actually doing everything you need to do in one go. You are wiping out the old period of 2pi and bringing it down to 1, and you are now inserting the new frequency. Now you would think by putting in 400 you would be making the period 400 long, but you aren't...you are making it 1/400 long, or 1/400 of a second, which means it gets 400 wavelengths (periods) through in 1 second....which is the definition of 400 Hz. By putting my frequency value in there, I am getting exactly what I want. So in this equation: y=sin (wx)), and w=2PI400, the 2pi gets rid of the old period of the cricle and brings it down to 1, and the 400 makes the new period/wavelength (they are the same thing) 1/400 of a second long. So if my frequency I want to demonstrate is 400 Hz, I would put y=sin(400(2pi)x) or y=sin (800PIx). The 2 PI gets rid of my normal 360 period and makes my new period 1, and the 400 (the T in the electrical equation) is making my new period 1/400. That is why frequency = 1/period, because when we use the term frequency we are saying how many wavelengths (periods) do we squeeze in there in 1 second. Visit desmos.com and fool around with y=cos(f(2PIx), and it will allow you to put a slider in for f...whatever frequency you set to f, the graph will show you the resulting graph.
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is the angular frequency similar to the inductive reactance?
The angular frequency = w
Inductive Reactance = wL
Sir can an ac graph (voltage vs time) be unsymmetric , I mean can the positive half and negative half can have different amplitude ....?????🤔🤔
Shifting the function along the vertical axis vertical axis is dc offset, but strange spikes in an oscilloscope's graph is typically noise.
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Nice. But what you call amplitude is magnitude. It does not vary whereas the sin wave variation plotted is the amplitude which changes.
For which level???
Link to the next lesson plz
Can someone PLEASE clarify. We were always told that electronic circuits are typically in DC…..why are we still talking about SIN and COS if we are in DC. This is very confusing. Is it Current that doesn’t shift positive or negative, or is it Voltage ???
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The equation V(t) = VmCos(wt + phi) you are saying Cos(wt +phi) varies between plus or minus 1, this implies that Vm is ALWAYS 1...is it correct to make that conclusion?
No, only the cos (or sin) varies between plus and minus 1.
I am busy with electrotechnics exams. . I have a question that you could possibly explain in a video please.
It says. The current equation for a circuit is i=200 sin 628t.
What are the values of:
1. Rms current
2. The frequency
3. The instantaneous value of the current when t is 2milli seconds.
Question 3. Is a problem for me. How do you calculate with time?
Help would be appreciated
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RMS=0. 707*i
2*pi*f=628, calculate for f
Substitute t=0.002 into your equation
Anyone knows the name of this gentleman ?
What types of job I can get with circuit analysis knowledge, besides teaching. I’m very bad at teaching?
Oh man i remember learning this in precalc like 3 years ago lmao
Plz mention other parts ...not found
No, that's the whole equation. Amplitude, angular velocity, time and phase shift are the variables that you need.
Very indepeth, I'm not trying to be an engineer just pass a cert exam. I understand alot but ot lost.
in my college, we learn with sine function, now im confused
You can convert between cos and sin with a pi/2 phase shift. But while we call signals sinusoidal it is really the real part of a complex exponential that we measure or observe in the physical world and the real part is the cosine.
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After 10 mins of you japping about nothing I got bored and just skipped 10 mins just to find out you still japping about the same nothing
Please talk in hindi language 😢
I found a Degree to Radians wheel showing Radians to Degrees via 𝝅 Pi since there not in alignment. Is there a different meaning to Radians Sin Wave you speak of?
See: en.wikipedia.org/wiki/Radian