How to obtain omega values from hertz

Thread Starter

KevinEamon

Joined Apr 9, 2017
284
This is probably going to seem like a V silly question but I can't think how to google it.

A single phase, 100 kVA, 11000/2200 V, 60 Hz transformer has the following parameters:
Rhv=6.0 Ω
Lhv=0.08
Lm(hv)=160
Rc(hv)=125 Ω
Rlv=0.28 Ω
Llv=0.0032
Obtain the equivalent circuit of the transformer:
a) Referred to the HV side
b) Referred to the LV side

So I created this schematic below. I went and found the formulas I need to convert everything, in order to answer the first question, these are the notation in red ink.



Problem is - all of the values for the inductors are in henry. I need to convert everything to complex numbers. Up till this point I pulled the value for Omega from the time notation, in the source.
H = jωL
But where to get the omega value from this?
My first instinct is to go for the hertz value.
Perhaps 1/60... Maybe...
Or perhaps it somehow derived from this complex power value...
 
Last edited:

WBahn

Joined Mar 31, 2012
29,979
There are 2π radians in a cycle.

1 Hz = (1 cycle / second)·(2π radians / cycle) = 2π radians/second

Hence the formula that we all rattle off (including me) SHOULD be written not as

ω = 2πf

but rather as


ω = (2π (rad/s)/Hz)·f

or

ω = (2π Hz·rad/s)·f

Now you plug in f, say 60 Hz, and the units work out beautifully as they should.

This is akin to having

D = 12 L

where L is in feet and D is in inches. That 12, while it is the ratio of two lengths, is NOT truly dimensionless. It is a conversion factor and thus needs to carry the ratio of the units it is converting to to the units it is converting from. It should be

D = (12 in/ft) · L

The conversion factor is 12 in/ft.

The exact same with that 2π. It is the ratio of two frequencies expressed in different units.

The conversion factor is 2π (rad/s)/Hz.
 

WBahn

Joined Mar 31, 2012
29,979
I hope you're not about to break into philosophy here Wbahn... What is t anyways? Lul thx guys
I'm quite serious. You asked if 't' was approximately 377(rads/s)/Hz. I have no idea if this is correct or not since I have no idea what YOU mean when you refer to 't'. It isn't time, since time has units of, well, time. Be it seconds or years or whatever.

About all that can be said for 377(rads/s)/Hz is that it is the ratio of two frequencies in which the numerator is a frequency sixty times greater than whatever the denominator is.
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
284
Indeed well It's always t on my question sheets. t in time domain... I wish I had the t to argue about it... but I need to get this dang assignment finished tonight. :) I have an exam next Friday... study study study...
 

WBahn

Joined Mar 31, 2012
29,979
Indeed well It's always t on my question sheets. t in time domain... I wish I had the t to argue about it... but I need to get this dang assignment finished tonight. :) I have an exam next Friday... study study study...
The variable 't' is almost always used to mean "time" (in this context -- certainly it means other things, like thickness, in others). It is a dimension variable whose units should evaluate to a measure of time.

The variables 'f' and 'ω' are two different variables for the same thing. While this certainly has some convenience to it, it many regards this is unfortunate because it leads people to believe that they are somehow fundamentally different quantities. They aren't It would be as if we called the length of the period of a waveform 'x' if it is measured in centimeters and 'y' if it is measured in inches and then memorize a formula that goes "x = 2.54·y" and then people would always be wondering if they needed this magic 2.54 in this formula or that formula. If we just always used a single variable, λ, for the wavelength then we can convert it to whatever unit of length we need to make the units work out properly. It would probably have been better in the long run if we had just settled on one or the other variable for frequency (I don't even care which -- flip a coin) and always used it when we needed frequency, scaling as needed to make the units work out properly. That is how virtually every other quantity is handled. I really can't think of any exceptions (at least in engineering/sciences world), although electromagneticists love to jockey things around and normalize them to make a bunch of dimensionless parameters.
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
284
Thanks Joey. I always take the time :) to read and reread what Wbahn says very carefully. Without him I doubt I'd still be on this course. Especially last year which was a significant learning curve for me.

You guys are all great and are part of any future succss I make.
 
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