Why is AC current represented with a sine wave?

[Pyral]

I understand that AC current looks like a sine wave when plotted on a graph, but why a sine wave? I could just as easily have it be a cosine function by having the wave reach its apex/trough at 0, and the general rising and falling pattern would still be present, and the period would be the same. Why did sine become the default wave form for describing AC?

Is there some mathematical reason that we use sine over cosine when describing AC current?

[JustMeHere]

It's the same wave you get when you spin a magnet past a coil.

[bob91343]

While it's true that a cosine wave begins at the crest, it's basically a sine wave.  It's easier to say and spell sine than cosine.

[Cerebus]

Using sine means that the amplitude is zero at zero phase angle. It's a lot easier to find the zero crossing of an arbitrary amplitude sinusoidal wave than it is to find a maxima or minima, as it would be with a cosine wave at zero phase. It's pure convention in the general case to choose sine over cosine, but the zero phase = zero amplitude just tips the logical balance in the favour of sine. Whichever you chose, the other will be along in a minute as soon as you introduce a reactance that causes a \$\frac{\pi}{2}\$ (90º) phase shift.

[CatalinaWOW]

I agree with Cerebus, it is strictly a convention.  And the roots of that convention may go back quite a ways.  In my trigonometry classes the sine function was introduced before the cosine function.  Again convention, but it may be because the sine function is more active around zero.  Plotting cosine for the first ten to fifteen degrees is pretty boring, especially in the days before calculators when you had to either directly measure triangles or go to a table. 

[rstofer]

I agree with Cerebus, it is strictly a convention.  And the roots of that convention may go back quite a ways.  In my trigonometry classes the sine function was introduced before the cosine function.  Again convention, but it may be because the sine function is more active around zero.  Plotting cosine for the first ten to fifteen degrees is pretty boring, especially in the days before calculators when you had to either directly measure triangles or go to a table.

Or use the ever-present slide rule.

Don't worry about the cosine being left out.  It comes back when you get to Fourier Series and both sin() and cos() appear in the same expression.

Equation 6 here:

https://mathworld.wolfram.com/FourierSeries.html

And, no, you don't need to know this stuff until you do.

It also shows up in vectors and phase shift problems.  Heck, it's all over the place!

[CatalinaWOW]

Still tedious with a slide rule, or early version calculator.  You had to pick a value, read off the function (or smash keys on calculator) and then put a point on graph paper.  Repeat until some shape shows or even better until some insight develops, like periodicity.   Plotting trig functions wasn't trivial until graphing calculators and then home computers came along.  (Or visa versa depending on how bleeding edge you were on your home computer).  And teaching modalities were established with those simple tools, long before the automated tools came along.

[rstofer]

Still tedious with a slide rule, or early version calculator.  You had to pick a value, read off the function (or smash keys on calculator) and then put a point on graph paper.  Repeat until some shape shows or even better until some insight develops, like periodicity.   Plotting trig functions wasn't trivial until graphing calculators and then home computers came along.  (Or visa versa depending on how bleeding edge you were on your home computer).  And teaching modalities were established with those simple tools, long before the automated tools came along.

You're right, of course.  The thing is, I graduated in '73 and the HP 35 came out in '72.  I had a 4 function calculator (very expensive) that was mains powered.  Pretty useless for classroom work.  The entire program was done with a slide rule.

Through my work, I had access to an IBM 1130 computer with a Calcomp 1627 plotter.  This was pretty useful for Bode' plots and such (we had the IBM Electronic Circuit Analysis Program - ECAP).  It was a blessing!

Still, the bulk of the work was done with tables and a slide rule.

I was an early adopter of the Altair 8800 and I had it up and useful before finishing grad school in '76.  I eventually added two 8" floppies and a Calcomp 1627 Plotter.  The golden age of computing - CP/M and Basic.  That was all turned on its head when UCSD released UCSD Pascal around 1980.  Now we had a real language!  Yes, C was around a little earlier...  Those were interesting times...

[Brumby]

I understand that AC current looks like a sine wave when plotted on a graph, but why a sine wave? I could just as easily have it be a cosine function...

Quite right.  There ARE two functions that could have been used - but:
 - using an arbitrary choice every time you wanted to describe something would result in confusion - so we pick one.
 - Sine is the basic function, cosine comes next - according to the etymology.  Cosine <= Complement + sine

Thus, sine is the logical choice and is the one that has become the convention ... but you could have a world built on cosine.

[Siwastaja]

Sine and cosine are the same function with offset in the argument.

It's far less confusing to use only one and specify the offset. This is because many more offsets than just 90deg exist in real life. For example, three-phase power uses offsets of 120 and 240 deg. Which one makes more sense:
sin(phi + 0)
sin(phi + 120 deg)
sin(phi + 240 deg)

or some strange mix:
sin(phi + 0)
cos(phi + 30 deg)
cos(phi + 150 deg)

In fact, one could argue that cosine just should not exist at all. Like the co in the name suggests, it's just a sort of variation of sine, short-hand for quicker writing when the argument happens to contain just the right offset.

[m k]

It's a height of a triangle in a unit circle.

[Cerebus]

It's a height of a triangle in a unit circle.

It never ceases to amaze me that some people can go through a whole school trigonometry course without a single teacher walking up to a black board, drawing a unit circle with its centre at the origin of a set of axes and pointing out what sine and cosine mean in that graphical context. In fact I can guarantee that someone reading this doesn't have a clue what I'm talking about because they had useless secondary school maths teachers. I've known loads of people who carry around a head full of trig identifies that they have learned by rote and have no clue why those identities are the way they are. Yet most people can derive them for themselves if you show them that diagram and point out how it relates to our old friend Pythagoras.

For the poor benighted souls with bad teachers who have never seen it:

[Terry Bites]

Simple harmonic motion that you learned about in school traces out a sinus curve. Just like that big whirly thing at the power station.https://www.google.co.uk/url?sa=i&url=https%3A%2F%2Fwww.shutterstock.com%2Fth%2Fimage-vector%2Fsimple-harmonic-motion-waves-1327229258&psig=AOvVaw0G0IZfPBY2-f6V3A3Afgig&ust=1644758121964000&source=images&cd=vfe&ved=0CAkQjhxqFwoTCPiyy86f-vUCFQAAAAAdAAAAABAK

Its usual to consider a pure tone in ac circuit analysis not a bunch of harmonics. Its not a convention, its how life is. All other cases are special cases of the pure sinusoidal.

[BeBuLamar]

How would one knows if the wave is a sine wave or cosine wave if the x coordinate isn't marked with degrees?

[Cerebus]

What x coordinate are you referring to?

[BeBuLamar]

To know if a wave is a sine or cosine you need to know the amplitude at the angle. The horizontal x axis is supposed to be labeled in angle and the vertical y axis is amplitude. So if you don't know when the waveform has the amplitude of 0 which angle it is at then you don't know if it's a sine or cosine wave.

[ledtester]

To me a "sine wave" is any function of the form y(t) = A*sin(w*t+d). Perhaps you can even add a constant and still call it a sine wave.

The "sine function" is just sin(t).

[Cerebus]

So if you don't know when the waveform has the amplitude of 0 which angle it is at then you don't know if it's a sine or cosine wave.

You can always tell when the amplitude of the sinusoidal part of a sinusoid is zero, even in the presence of an offset, it's the when the wave crosses the midpoint between the peaks and troughs.. Whether you model a sinusoid as a sine wave or cosine wave is purely a matter of convenience and convention. The only time you're going to care about the phase angle in an absolute sense is when there's a physical angle involved, as in a motor or generator. The rest of the time you're just concerned with an abstract \$y = A \sin (\omega t + \phi)\$

[BeBuLamar]

But without the marking on the x axis how do you know the zero amplitude point is 0 degree or 90 degree?

[Cerebus]

But without the marking on the x axis how do you know the zero amplitude point is 0 degree or 90 degree?

Do we care? As sin and cosine waves have exactly the same shape they will behave exactly the same. You seem to be getting caught up in a mathematical model of the real world as if it was the real world.

Again, it is just a convenience for us to use sine so that a wave starts at zero when \$t\$ is zero when we're modelling some signal of amplitude \$A\$ and frequency \$f\$ as \$A \sin (\omega t)\$ (where \$\omega\$ is \$2\pi f\$).

[gf]

To me a "sine wave" is any function of the form y(t) = A*sin(w*t+d). Perhaps you can even add a constant and still call it a sine wave.

My understanding,  too. And y(t)=sin(w*t) and y(t)=cos(w*t)=sin(w*t+pi/2) are just two special cases thereof, for d=0 and d=pi/2. In many cases, absolute phase does not matter. What mostly matters is rather the phase difference between two sine waves sin(w*t+d1) and sin(w*t+d2), which is d2-d1.

[BeBuLamar]

But without the marking on the x axis how do you know the zero amplitude point is 0 degree or 90 degree?

Do we care? As sin and cosine waves have exactly the same shape they will behave exactly the same. You seem to be getting caught up in a mathematical model of the real world as if it was the real world.

Again, it is just a convenience for us to use sine so that a wave starts at zero when \$t\$ is zero when we're modelling some signal of amplitude \$A\$ and frequency \$f\$ as \$A \sin (\omega t)\$ (where \$\omega\$ is \$2\pi f\$).

that is my answer to the OP how do the OP know they represented the AC current with a sine wave and not cosine wave?

[Vovk_Z]

I guess we use sine to plot on a graph but not cosine because the sine wave has both full half-cycles - an entire positive half-cycle and an entire negative half-cycle.
When we plot the cosine wave it looks like a "V" letter - a positive quarter-cycle, then full negative half-cycle, and then positive quarter-cycle again. So it may not show the alternating nature of an electric current in the best way.

[TimFox]

By the way, "AC current" is redundant.

[ledtester]

that is my answer to the OP how do the OP know they represented the AC current with a sine wave and not cosine wave?

Define "cosine wave" and maybe we can resolve this.

[Vovk_Z]

By the way, "AC current" is redundant.

I'm not talking about that post, but rather in general:
I may be wrong but I guess we use this a bit redundant form of "AC current" because we use "AC voltage" too, so we add "current" to "AC" when we want to say that we are talking about a current but not about a voltage.   

[Siwastaja]

By the way, "AC current" is redundant.

No, it's not. "AC" has developed a set of completely new meanings which have nothing to do with current, and just become a term of its own. "AC voltage", "AC current", "AC component" are all widely used and understood, not only colloquially but rigorously scientifically, and they can't be written open like "alternating current voltage", "alternating current current" and "alternating current component", obviously. Why? Because "AC" in such contexts does not mean "alternating current".

[tooki]

By the way, "AC current" is redundant.

Except not really. As others have explained, “AC” just refers to alternating current in the abstract (it means the entire concept of electricity whose polarity changes constantly), not to “current” in the narrow engineering/physics sense. You’re not going to convince anyone that our multimeters should say DV, DC, AV, and AC on the dial (for DC V, DC I, AC V, and AC I, respectively).

English is happy using many, many redundant abbreviations/initialisms (LCD display, PIN number, etc).

Some languages, like German, expressly discourage them, resulting in awkward constructs like “LC-Display” and “ISB-Nummer” (the latter of which really irks me because there is an internal hierarchy to the 4 words in ISBN, and “ISB-Nummer” violates the hierarchy by plucking out a word from a deeper level: structurally, it’s “international+(standard+(book number))”).

[Gyro]

By the way, "AC current" is redundant.

Unless you can persuade the world to adopt AV as a standard abbreviation for Alternating Voltage, we are stuck with 'Alternating Current voltage' and 'Alternating Current current'.


Edit: ... and as tooki says, DV too.

[m k]

Many times I find myself changing AC to local expression of AE, where E is electricity.
Or more closer WE, where W is wall.

My head is also so tightly in DC side that my intuitive wall electricity peak value is wrong.
Of course the reminder is pretty instant but it's not a value, it's a picture of a scope screen with almost vertical lines.
Values become later, if ever.

[golden_labels]

To add to “it’s a convention” comment: using a sinusoid is a convention too. One does not only choose a specific point to be t=0, but also chooses to ignore what happens sufficiently far away from that point. Sine wave extends infinitely far in both directions, which does not happen with any real-world signal. So it’s all about saying “look, around that point we observe that frequency” and, if more than one sinusoid is considered, “look, they differ in phase that and that way”. Whatever choice serves that purpose best is the right one.

[TimFox]

To my many respondents:  don't worry, I find it very difficult to avoid "AC current" in technical writing.  It is still redundant, as is "Gobi Desert" (another pleonasm).

[tooki]

To my many respondents:  don't worry, I find it very difficult to avoid "AC current" in technical writing.  It is still redundant, …

No it isn’t. The “current” in “AC” doesn’t mean the amount of flow. It’s referring to the abstract concept of electrical flow, for the purposes of describing what type it it. So the phrase “AC current” generally means “flow rate of an alternating current”.

When we want to refer to the abstract current itself, as I did above, we do not abbreviate it, and we use a pronoun: an alternating current. You’d never refer to it as “an AC”.

[TimFox]

"Redundant" does not mean "incorrect", "negating", or "oxymoron"--it just means "unnecessary for meaning".
Others include "PIN number" that you mentioned:  the concept is still understood.
A common expression in English technical writing is "3.2 A rms AC", which could be written "3.2 A rms AC current".

[JohanH]

Because "AC" in such contexts does not mean "alternating current".

And yet it might. Because it isn't a standardized abbreviation or term. Edit. It is, but it isn't always used correctly.

[tooki]

Because "AC" in such contexts does not mean "alternating current".

And yet it might. Because it isn't a standardized abbreviation or term.

That’s an absolutely absurd claim.

[JohanH]

That’s an absolutely absurd claim.

I might have missed it, I haven't read all standards. Care to quote?

[tooki]

That’s an absolutely absurd claim.

I might have missed it, I haven't read all standards. Care to quote?

You sound like Bill Clinton arguing the meaning of “is”.

We can argue about what the exact meanings of “alternating current” are, but you only look like a fool trying to argue whether “AC” stands for “alternating current” in the context of electricity.

[TimFox]

I seem to have stirred up a flurry amongst the language snowflakes.

[JohanH]

We can argue about what the exact meanings of “alternating current” are, but you only look like a fool trying to argue whether “AC” stands for “alternating current” in the context of electricity.

That was not my intention. The thought behind my post is whether "AC" as a term has been used in an ambiguous ways not defined in standards. I do find it mentioned in IEC IEV 151-15-01.

Note 3 – For the marking of electric equipment, either the notation AC (see IEC 61293) or the graphical symbol ~ (see IEC 60417 item 5032) may be used. Example: AC 500 V or ~ 500 V.

Note 4 – According to ISO 31-0 and IEC 60027-1, unit names and unit symbols shall not be qualified by "AC" as an attachment. Example: U_AC = 500 V is correct, U = 500 V_AC or U = 500 V AC are incorrect.

   

So it is comparable to the "~" sign. But it is not allowed to use "AC" as a unit (attachment).

The common usage VAC and IAC (and variations) is thus wrong.

So I cannot see that there is a fully satisfying situation with regards to standards.

[CatalinaWOW]

For those uncomfortable with the use of AC as a descriptor what is your preferred way to describe and differentiate in situations where there is both a zero frequency component and also current at a single dominant frequency?  The use of AC and DC is usually very clear in context and the situation is not uncommon..

[xrunner]

A lot of instruments use symbols. Such as this example from a Fluke 117. Again the sine wave for alternating volts or amps, and the stable line above a ground for non-alternating voltage or current.

[CatalinaWOW]

That is fine for an instrument, and probably could work in written communication (with some typography issues) but how do you pronounce those symbols in spoken conversation or in a lecture?

[Siwastaja]

DC and AC are used in contexts such as DCT transforms in JPEG images to differentiate between the zero-frequency component (put simply, same color across the macroblock) and higher frequency components (varying color across the macroblock). If you think about it in power line terms, it sounds ridiculous, but this is what it is. Language lawyerism is futile; reality wins over theory, especially if it's so widely accepted both in colloquial and scientific use as AC/DC terms are.

[Siwastaja]

That is fine for an instrument, and probably could work in written communication (with some typography issues) but how do you pronounce those symbols in spoken conversation or in a lecture?

"AC voltage range", for example. This is unimportant; the lecturer needs to carefully explain what the meter actually measures, anyway, and this is far beyond just one simple term: does it measure RMS? Average? Peak? Peak from which RMS is calculated assuming sine waveform? Something else? In presence of DC offset, how does it behave? Is there a maximum frequency limitation? And so on, and so on.

After that, the choice of exact term is unimportant, it's just an identifier.

The lecturer would also make clear that a multimeter AC functionality is a very limited instrument and oscilloscope should be used to see all the details of the actual waveform.

[SandyCox]

sine is cosine with a phase lag of 90 degrees.

Must textbooks use cosine as their phase reference.

[Vovk_Z]

I seem to have stirred up a flurry amongst the language snowflakes.

That's because we don't really know about a topic question, but we always know when somebody is wrong on the internet.  ( )

[Vovk_Z]

sine is cosine with a phase lag of 90 degrees.

Sine is just more beautiful. That's it. 

[Cerebus]

sine is cosine with a phase lag of 90 degrees.

Sine is just more beautiful. That's it.

Not so. In human perception more beautiful is generally associated with symmetry, with symmetrical being seen as more beautiful than asymmetrical. Vis:

If you start at the origin a sine wave is perceptually asymmetric, a cosine wave symmetric:



corresponding to asymmetric and symmetric perceptions of natural beauty:

[newbrain]

I've known loads of people who carry around a head full of trig identifies that they have learned by rote and have no clue why those identities are the way they are.

This is a terrible way of learning, and it can happen due to faulty teaching but sometimes also due to some student's attitude.

Quite a bit OT, but relevant:
During the "Sequential and Combinatory Systems" course at my uni, we were studying among many things (the usual: Karnaugh maps, Mealy and Moore FSMs etc. etc.) Z80 assembler programming.

A friend and colleague, smart and with very good marks, came to visit.
He was flabbergasted when I explained that the board in front of him was a tangible, real Z80 with RAM, EPROM etc.
"Oh, I'd never have thought that this thing existed!"

For him the instruction set, ROM, RAM and ports were all just a conceptual exercise - bearing no relation whatsoever with the physical world - he had categorized it more or less as an overly complicated, abstract, way of representing state machines.