# Phasor circuit question

#### lurikeen

Joined Apr 13, 2011
5
I've been working on the following phasor circuit problem, but the results seem incorrect to me, because I get one of the currents, I2, to be to be 0A when it appears that it shouldn't be. I am solving using the mesh current method.

My equations, where x=I1, y=I2, and z=I3:

This outputs I3=-3i, I2=0. I can't see how this is correct.

Link to the equations on wolfram alpha: http://www.wolframalpha.com/input/?i=solve+x%3D5%2C+0+%3D+-5i+%2B+%28y-x%292i+%2B+%5By-z%5D5%2C+0%3D%5Bz-y%5D5+%2B+%5Bz-x%5D%5B-3i%5D+%2B+%5Bz%5D3i+for+z

Can anyone help me find my error? I don't have the solutions but I think its wrong. Thanks.

#### t_n_k

Joined Mar 6, 2009
5,455
Your solution is correct. It's certainly possible that the circuit conditions allow for zero current draw from the voltage source. In effect it doesn't matter if the voltage source is there or not.

#### steveb

Joined Jul 3, 2008
2,436
I've been working on the following phasor circuit problem, but the results seem incorrect to me, because I get one of the currents, I2, to be to be 0A when it appears that it shouldn't be. I am solving using the mesh current method.

My equations, where x=I1, y=I2, and z=I3:

This outputs I3=-3i, I2=0. I can't see how this is correct.

Link to the equations on wolfram alpha: http://www.wolframalpha.com/input/?i=solve+x%3D5%2C+0+%3D+-5i+%2B+%28y-x%292i+%2B+%5By-z%5D5%2C+0%3D%5Bz-y%5D5+%2B+%5Bz-x%5D%5B-3i%5D+%2B+%5Bz%5D3i+for+z

Can anyone help me find my error? I don't have the solutions but I think its wrong. Thanks.

#### lurikeen

Joined Apr 13, 2011
5
Well, since its a constant voltage source, I just felt that the chance that it would have no current running through it was very low. I've just started with complex numbers, so I really don't understand exactly what is MEANT by the solution -3i, or the voltage on the source of -5i.

Thanks btw.

#### steveb

Joined Jul 3, 2008
2,436
Well, since its a constant voltage source, I just felt that the chance that it would have no current running through it was very low.
Well, actually you are correct about that, if you consider a real world example. However, mathematically, a zero current is no problem. Basically, what is happening is that the current source is supplying the power to the circuit and just happens to produce a voltage (at the terminals of the voltage supply) perfectly equal to the supply voltage. Hence, the voltage source doesn't need to supply current to force the constraint that the voltage across the terminals is -5j. Note that in the real world, such perfect balancing does not happen. There would always be a small current coming from (or going into) the voltage supply.

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