- #1
- 295
- 4
Homework Statement
Homework Equations
The Attempt at a Solution
So far I was able to transform each element into the frequency domain:
I am just unsure how to work with the dots to find the mesh currents. Can someone explain? Thanks.
I believe we have studied this but I am definitely not clear on the subject.Have you studied dependent sources?
In circuits with mutual inductance, you represent mutually induced emf using current controlled voltage source(s).
Ok. Think about what the dot convention means here.I believe we have studied this but I am definitely not clear on the subject.
Negative since it is leaving ?Ok. Think about what the dot convention means here.
When the current "enters" a coil at the dot, the dotted terminal of the other coil becomes positive i.e.both the dots become positive (and negative) simultaneously.
You have assumed i2 "leaving" the dot of the 6H coil. What will be the polarity of the dot?
Yes. So what is the polarity of the dot of the 8H coil? That would be the polarity of the mutual voltage induced in the 8H coil.i.e. the emf induced in 8H coil due to the current in the 6H coil. Add a current controlled voltage source in series with the 8H coil with the polarity you just found. Controlling current would be i2 for mutual emf in the 8H coil and i1-i2 for mutual emf in the 6H coil.Negative since it is leaving ?
Would these be the two equations?Yes. So what is the polarity of the dot of the 8H coil? That would be the polarity of the mutual voltage induced in the 8H coil.i.e. the emf induced in 8H coil due to the current in the 6H coil. Add a current controlled voltage source in series with the 8H coil with the polarity you just found. Controlling current would be i2 for mutual emf in the 8H coil and i1-i2 for mutual emf in the 6H coil.
Thanks for such a complete answer. One more question. Can you always attach the mutual inductance voltage source by the negative end to the dot? For example in this circuit:Your calculation of Zc is not correct. Zc should be of comparable magnitude to the other impedances in the circuit.
Your first loop equation does not include a mutual inductance term, and the signs for the currents flowing through the j200 inductor are not correct.
For your second loop you didn't account for I1's contribution to a mutual inductance term, and I2 should make two contributions (I2 flows through both inductors, hence though both dots).
I find that it can be helpful to re-draw the circuit with the mutual inductance inspired voltage sources inserted. Start out with them having their negative ends anchored to the dot of their inductor. Figure out their values by using labelled currents and the dots to assign appropriate signs (after which you can adjust the voltage source directions to eliminate negative terms if you wish), then write the loop equations. This way you can't drop terms if you do your KVL walks methodically around the loops.
View attachment 113697