But you have pretty conclusively established, via multiple approaches, that all three voltage sources must be identically zero. So there's really only two possible conclusions -- the question, as stated, has no solution, or you are not interpreting the question the way it was meant to be interpreted. If the latter, it could be that the question has some subtle point that you are missing, or it could be that whoever wrote it phased it in such a way that it doesn't convey what they meant it to.

Present you findings to the instructor and ask for clarification.

I am self studying. I have no instructor.

Amazingly, it looks like there actually is a non-zero solution. If you can't figure it out we can go through the calculations eventually. It looks like there is a very simple proof though that does not involve mesh equations but that would just prove that there is a solution.

A hint that might help is that we must have this satisfied:
V1+V2+V3=0

That means that one of these must be true:
V1+V2=-V3
V1+V3=-V2
V2+V3=-V1

and that means that ONE source can be removed from the circuit and we are still be able to find the solution.
Try writing the equations with that in mind and see what you can get. You may have to try all three sources in turn if you don't see the right one to eliminate right off.

I think that reduces the number of equations to 3. The only question then is, is this reduction allowed by the instructor.

Because of the redundant source and the need for mesh analysis, this may require an analysis using the idea of a supermesh. You could check that out for more information.

Because of the topology change in that solution, that may actually remove one of the currents as well and that may not be allowed because it is possible that the associated current will then not be zero, only the other three. I'll look into this further.

It looks like if we solve for the currents using only two of the voltages in a full analysis without any other changes, we can then solve for one of the two voltages in terms of only one voltage. If we then insert that into all four equations we only get a zero for only one of the currents. This is no matter which one we solve for the second voltage. That indicates that there is no solution it it's exact form. If we got two zero currents we could at least say that, but it looks like we don't even get two currents that can be zero.

Now the question is why was this problem given in this manner. Could the wording of the problem be incorrect?
I don't think so, but it may be that our interpretation of the problem statement could be wrong.

When I re-read the statement, I see that the object is that the current through EACH resistor must be zero, NOT the mesh currents themselves.
Looks like we have to start over
This means we don't zero i1, i2, i3, i4 we have to have iR2, iR3, iR5, and iR7 zero instead. This might change things.

sorry , when i said if we zero out all the currents , i meant the resistor currents themselves. resistor currents can only be zero if and only if all the mesh currents are equal. And this way too voltage sources come out 0V.

 

I am self studying. I have no instructor.

So where did this exercise come from? Is it from a source that is available in electronic form so that we can take a look at it? Or could you take pictures of the actual problem and post them (and provide direct translation of non-English text involved)?

 

I am self studying. I have no instructor.

sorry , when i said if we zero out all the currents , i meant the resistor currents themselves. resistor currents can only be zero if and only if all the mesh currents are equal. And this way too voltage sources come out 0V.

Hi,

Yes, I was solving for the resistor currents now not the mesh currents. I was not able to find a non zero solution in the allotted time.

Since everyone here seems to have found that same result, the question came up if the problem was presented properly. If it was obtained from a book it is entirely possible that the book is wrong. Technical books can be wrong, and I've found mistakes in many of the books I've read. It could be just the wording or the goal or something else.

I might try one more attempt at this just to be sure. I'll use an entirely different method.