# Radians to measure ac currents

1. Nov 7, 2014

### EngUOL

Could someone please explain why is chosen to measure ac sin/cos signals with radians instead of seconds? If ac waves is the behavior of a wave over time???

Any feedback would be appreciated. Thank you!

2. Nov 7, 2014

### EngUOL

Sorry I know that is a stupid question to ask. But I got that concept missing. tHanks again

3. Nov 7, 2014

### zoki85

Why do we measure lenght in units like meters and time in units like seconds hmm...

4. Nov 7, 2014

### EngUOL

No zoom I mean why is graphs in ac theory measured in radians instead of time. Like an amplitude against radians(wt) graph would it be amplitude against seconds? Or radians can be converted to seconds???

5. Nov 7, 2014

Zoky sorry

6. Nov 7, 2014

### zoki85

Argument must be naked number, or formally radian*.
Don't you think it will be unusual to try to calculate something like cos(1second)?

*Known reduction are degrees ( ° ), but we know it is per definition 2π = 360°

7. Nov 7, 2014

### EngUOL

Thanks zoki. Ok so it's a matter of making things easier. The use of radians is just a more efficient measurement unit for waves. Is that right??

8. Nov 7, 2014

### zoki85

Well, if you know how to convert t=1second to radians than you can do it

9. Nov 7, 2014

### EngUOL

Zoki i know that im a completely dumb head lol but i dont understand the point of using radians instead of seconds.i have seen voltage over time graphs. but ive seen amplitude over radians graph. is radians another unit to measure time in this second case??

10. Nov 7, 2014

### zoki85

How are defined trig functions sin and cos ? What is their argument? How is defined an arc ?

11. Nov 7, 2014

### psparky

Well, 60 hz is the same is 60 cycles per second.

Ok. Radians simply take that number then multiply it by 2π. 2π is one complete rotation of a circle, or of a cycle.

So, for example, the frequency for electricity is often 60 hz or 60 cycles per second as I mention above.

When you look at a sin wave of electricity, a single phase 120 volt system at 60 hz is represented by this:
170sin(377t)
170 is peak to peak.....120 is RMS.

The figure 377 is obtained by multiplying 60*2π.

If you use this figure for example, 170sin(60t), your sin wave will be way off!

Most things in engineering and physics seem to work easier with the radians per second. But regardless, if a question is asked in the frequency domain, sometimes it's better just to leave it there. If it's asked in radians it may be easier to keep it there.

Say you are given a transfer function of 1/(jω+1), it makes sense just to leave it like that and plug in your radians per second.

You also need to be careful whether you are using radians or degrees. If you calculator is in degrees rather than radians in some cases, you will be wrong!!! Visa versa for the other way.

There is more to it than I am saying, but that should start you on your way. This takes a while to figure out, let it come naturally over time.

Last edited: Nov 7, 2014
12. Nov 7, 2014

### EngUOL

very appreciated psparky. yea that kind of make sense. thanks a lot!

13. Nov 7, 2014

### zoki85

EnqUOL, how is defined an angle?

14. Nov 7, 2014

### EngUOL

you tell me zoki

regards

15. Nov 7, 2014

### zoki85

Angle is a ratio of corresponding arc lenght and radius on given circle. This ratio is argument of trigonometric function. That's the whole philosophy.

16. Nov 7, 2014

### sophiecentaur

When we first did Calculus at school we were told that differentiating sin(x) gave you cos(x) as long as x was in radians. If you accept that as a fact of life then the rest follows. That may strike one as being unsatisfactory but the simple statement helped us through until we had gone way past learning the calculus of simple trig functions.
Fact is that 'degrees' are a totally arbitrary way of chopping up a circle so it isn't surprising that using such an arbitrary measure can get you into difficulties and lumpy extra constants. The radian is not arbitrary; I always say that the inhabitants of the planet Zog could be using 128 of their degrees in a circle but they will still be using Radians when they do their proper maths.

17. Nov 8, 2014

Also - radians are a measure of "around the cycle" - and this is relative to typically one of the items you are discussing ( Phase A of a three phase system for example) - if you want to use "time" this becomes VERY arbitrary.... as well when talking about AC we are typically talking about steady state. If you want to discuss a short circuit - then t=0 is very well understood ( and often used) - but that is a special case,
But for some system in the AC world we reference something as "0" - all other parameters are referenced back to that, like the Phase A. Look up a 3 phase phasor diagram... if you used a t=0 this diagram would look different every time - and be more complicated.

18. Nov 8, 2014

### sophiecentaur

If you choose to use t, to specify a point on a waveform, then you must use a specific Unit (seconds or whatever), which will soon get you into a mess because you then need to refer it to the period of the waveform etc. etc.. Using Phase, in Radians (of course), the problem does not arise.
Sometimes, for practical reasons and in a particular context, Time is used, but it would be necessary to convert back to phase for any general conclusions to be gained from an experiment or measurement.
I know people will react against the apparent aggravation of getting to grips with Radians but one just has to grasp the nettle and get used to the little devils. You really can't do without them.

19. Nov 8, 2014

### EngUOL

thanks a lot. best comment about my question so far. thanks to everyone thou!!!

20. Nov 9, 2014

### jim hardy

It has become so widely accepted that we forget how we got here.
I think it was Steinmetz who first used complex numbers to represent cyclic voltages.

One's first instructor should take one through this diagram:

which paints in one's mind the relation between a wire loop rotating in a magnetic field and the voltage that results

and how natural is the relation between time and angle.
It becomes intuitive so soon that we old guys sometimes forget to introduce newcomers to it.

Now: sine function is a mathematical oddity because when you differentiate it its shape doesn't change
but it shows up all the time in physics, Mother Nature seems quite enamored of it...
And it shows up often in Mathematics (try a search on Euler). I suppose Mother Nature made mathematics too....

So it is the accepted "coin of the realm" in electrical engineering
Sharpen your skills with it early on.
As the kids say nowadays, "Just Do It".

old jim

21. Nov 9, 2014

### zoki85

Hehe, " Noli turbare circulos meos! "

22. Nov 9, 2014

### sophiecentaur

If you were to come over here, your times would all be wrong though - even though your π and my π would be the same. (Also the engineers on planet zog)

23. Nov 10, 2014

### jim hardy

Times all wrong ? hmmmm..

indeed i woke up last night realizing my wire loop analogy is likely off a quarter turn from the image i picked...

You guys over there don't have Whitworth phasors or something , do you ?

Ahhhh now think i see what you mean - the diagram i picked shows ωt pointing to a phasor labelled 30° not π/6 radians.
Yet ω is defined at top as radians/sec.....
One must decide at start of every exercise what units he'll use, degrees or radians.
Rigor is the price of preciseness in understanding?

Thank heaven for Pi !

old jim