Homework Help: Transformer & Mesh Current Problem

1. May 13, 2014

Cetullah

Hello people, I ve recently started to solve questions about magnetic coupled circuits, but I am stuck at a question that I ve seen for first time. I want to write the mesh equations but I simply dont know what should I do with the transformator in the middle when writing the equation for upper mesh. I seek your guidance, thank you.

The question is in the attachment.

Attached Files:

• soru.png
File size:
3.6 KB
Views:
353
2. May 13, 2014

Staff: Mentor

Do you know the AC transfer function for a transformer? Usually the turns ratio will be listed, but I'm guessing that is just a 1:1 transformer. Do you understand the meaning of the two dots shown on the transformer?

3. May 13, 2014

tarakan

What do the dots mean? Is it CW vs CCW windings?
Positive becomes negative and negative becomes positive?

4. May 13, 2014

Staff: Mentor

Yes, the dots indicate the polarity of the input and output AC voltages. If the dots are both at the top, then the output voltage waveform is in phase with the input voltage waveform. If the dots are on opposite ends like in this figure, then the AC output voltage waveform is 180 degrees out of phase with the input voltage waveform.

Can you take a cut at the mesh KVL or node KCL equations now...?

5. May 13, 2014

tarakan

I would use a SPICE simulator for that, personally.
Even if I know how to solve for resistor grids, what resistance do transformer windings offer?
What is the shift in current /voltage in this 'ideal' transformer?
Thanks.

6. May 13, 2014

Cetullah

Hello, it is seen on the picture that its 1:2. :) And I didnt understand what you meant with transfer function :( You mean those stuff with complex variables (s)? Or is there a formula?

7. May 13, 2014

Staff: Mentor

Ah, I missed the 1:2. By transfer function, I just mean how the AC voltage makes it through an ideal transformer. Does the amplitude change and phase inversion make sense to you? Can you start writing the equations now?

8. May 13, 2014

The Electrician

Don't use the upper "mesh". Use the loop comprised of the periphery of the circuit, along with the left and right meshes.

Also, you probably will need to assume that the two transformer windings are perfectly coupled so that the mutual inductance, m, is just SQRT(L*4L) = 2L, where L is the inductance of the left winding and 4L is the inductance of the right winding. It may be reasonable to assume that the DC resistance of both windings is zero.

9. May 13, 2014

rude man

Assume the transformer is ideal, then L and 4L don't enter the picture. Just assume the secondary voltage is 2x the primary voltage and the secondary current is 1/2 the primary current. The rest should be straightforward. As berkeman pointed out in post #2, observe the polarity due to the dots.

10. May 13, 2014

The Electrician

The OP said "I want to write the mesh equations..."

Your recommended assumptions can certainly lead to an ad hoc solution with the additional assumption that the transformer is ideal, but how can they be included in mesh equations such that all the equations remain mesh (or loop) equations?

11. May 13, 2014

tarakan

Can this circuit be represented like this at avrious stages of the AC cycle?

We are solving for RMS? "Rectified" voltage on that resistor. Am I correct?

AC on the primary and on the secondary of a transformer is in phase?

http://en.wikipedia.org/wiki/Transformer: [Broken]
"With sinusoidal supply, core flux lags the induced emf by 90°."
Is this part of the ideal model? Exactly 90° or is it ignored?

Does this cause transformers to shift phase ≈90° between primary and secondary?

I was taught to draw a DC analogs for AC circuits.
I am not an expert, I had a similar problem 5 years ago in college and failed an exam because I never solved it.

Last edited by a moderator: May 6, 2017
12. May 14, 2014

rude man

I would go with summing currents to zero at 3 independent nodes. 3 equations, 3 unknowns plus the transformer voltage and current relations I gave. In fact, I already have. The result for the output voltage is quite elaborate, but I don't think any other method would be better.

I see no impediment to writing 3 mesh equations if that is what is insisted upon. Since the OP did not label his resistors I can't describe them readily but they should be obvious: 1 includes the primary, one around 3 outside resistors, and the third includes the secondary. Wouldn't do it that way myself & don't see why the OP should either.

13. May 14, 2014

rude man

Never heard of drawing dc analogs. Sounds dangerous! Certainly would not work if a non-ideal transformer is assumed.

Anway there is no phase shift betw. primary and secondary voltage or current except possibly 180 deg. Primary and secondary inductances are assumed infinite, leakage fluxes and lead resistances zero. Coupling is unity.

Last edited by a moderator: May 6, 2017
14. May 29, 2014

tarakan

So can I use this model to solve a problem that Cetullah posted?

15. May 29, 2014

rude man

You mean assume an ideal transformer I hope? As I said, I'd forget any dc analog model asap.
Assume an ideal transformer unless someone tells you differently.

You can use KVL or KCL or any other valid method of analysis.

16. May 29, 2014

tarakan

But I don't know how to treat the 8 ohm resistor that this problem is about. It is neither part of primary nor the secondary circuit.

17. May 29, 2014

rude man

Treat it like any other component. It's part of the circuit, what's the problem?

The transformer is just a device where output current is 1/N times the input current and output voltage is N times the input voltage. In your case N=2. That is all you need to solve the equations, whether you use KCL, KVL or whatever (I personally always sum currents at each independent node to zero).

18. May 30, 2014

tarakan

How can I sum currents in every node if there are two different current sources and they are tied with a resistor that has effect on both nodes? To sum currents to zero they all need a sign (+ or -). I don't understand this either.

I took a class on this to get a piece of paper that determines one's social status, but I had no time to learn subjects in depth while in college.

Thank you for trying to help me, Rude Man!

Last edited: May 30, 2014
19. May 30, 2014

rude man

OK, I'm going to give you one nodal equation, the one at the transformer primary V1.

Let

V1 = xfmr. primary high (dotted end)
V2 = xfmr. secondary high (not the dotted end)
V3 = right-hand node (3 resistors meet)
i1 = current flowing into xfmr primary dotted end
i2 = current flowing into xfmr secondary dotted end
Then you can write 5 equations in 5 unknowns: V1, V2, V3, i1 and i2.
Here's the first one for you:

(60 - V1)/4Ω = I1 + (V1 - V3)/8Ω

This is a KVL equation or close to it (I don't pay attention to nomenclature; I I just sum currents to zero at each independent node). Now come up with the other four. Remember what I said about the relationship betw. i1/i2 and V1/V2 for an ideal transformer; that's 2 equations.

20. May 30, 2014

tarakan

V1 = {I1 + [( (V1-V3)/8Ω)*4Ω)-60} * (-1)

V2 = (-2) * {I1 + [( (V1-V3)/8Ω)*4Ω)-60}

I1 = ( (V1-V3)/8Ω) *4Ω -60+V1

I2 = { ( (V1-V3)/8Ω) *4Ω -60+V1 }/2

I will finish V3 tomorrow. Than I solve a system of equations by substitution and it is solved?

Thank you.

21. May 30, 2014

rude man

That's the idea. You can substitute I2 = 0.5 I1 and V2 = -2 V1 to reduce your equations to a more manageable three (in V1, V3 and I1 only). Use Wolfram Alpha or other software to avoid math mistakes. That way you don't need to rewrite all your equations for V2, I1, I2 etc. the way you did, thereby avoiding math errors. The idea is to concentrate on making sure you have the original equations correct, then leave the math to software.

(Check I2. I2 goes into the dotted end so the current going into the top end is -I2.)

Last edited: May 30, 2014
22. May 30, 2014

The Electrician

Why solve for 5 unknowns? The problem is to solve for the voltage across the 8Ω resistor so all that is needed is V1 and V3. Two equations in two unknowns would seem to be sufficient.

23. May 30, 2014

rude man

I didn't say to solve for 5 unknowns. I said to solve 5 equations and obviously if you only need V3 then that's the only one you solve for.

The equations for 5 unknowns are there whether you like them or not. You cannot solve a 5-variable problem with 2 equations.

24. May 30, 2014

tarakan

I know that.

Thank you for helping me.

Transformer winding 1 has no resistance or infinite resistance?
What is the current flowing through?
Thanks.

25. May 30, 2014

tarakan

If I short the secondary, the current through the short will be infinite even though it is 1/2 of the primary current?
Thanks.
This is my last question because I still don't understand what I am doing.