Hi, I'm pretty new to circuits and I'm trying to solve the following textbook problem:
I was able to find the equivalent resistance and source current (I = 2.14 A), but the problem arises when I try to keep track of which wire Io is flowing through as I simplify the circuit.
First I wyedelta transformed the 8,12,12 ohm resistor connection on the left and simplified the circuit to something like this:
Now apparently the current in the blue wire corresponds to Io from the problem, and I can kind of see that since in the original, Io is between the 8 and 14 ohm resistor connection, and here Io is also between the same two resistor connections (albeit the 8 ohm resistor turns into a 28 ohm one from the transformation).
However when I further simplify the circuit to this:
Apparently this blue wire also corresponds to the wire Io flows through. I don't understand why that's the case; intuitively for me at least, the current in this particular wire should be completely different than the current in the blue wire in the second image. In the second image, it looks like the addition of the 1.3A current and the current from the 14 ohm resistor should equal the source current, yet the third image implies that the 1.3A current and the far left 28 ohm current equals the source current.
Is there some sort of trick to tell which wire carries the current Io throughout simplification?
(Also as an aside, is there any reason why I can't apply current division to the 28 and 14 ohm parallel resistors in the second image? Is it because the current is also being split to the farleft 28 ohm resistor?)
I was able to find the equivalent resistance and source current (I = 2.14 A), but the problem arises when I try to keep track of which wire Io is flowing through as I simplify the circuit.
First I wyedelta transformed the 8,12,12 ohm resistor connection on the left and simplified the circuit to something like this:
Now apparently the current in the blue wire corresponds to Io from the problem, and I can kind of see that since in the original, Io is between the 8 and 14 ohm resistor connection, and here Io is also between the same two resistor connections (albeit the 8 ohm resistor turns into a 28 ohm one from the transformation).
However when I further simplify the circuit to this:
Apparently this blue wire also corresponds to the wire Io flows through. I don't understand why that's the case; intuitively for me at least, the current in this particular wire should be completely different than the current in the blue wire in the second image. In the second image, it looks like the addition of the 1.3A current and the current from the 14 ohm resistor should equal the source current, yet the third image implies that the 1.3A current and the far left 28 ohm current equals the source current.
Is there some sort of trick to tell which wire carries the current Io throughout simplification?
(Also as an aside, is there any reason why I can't apply current division to the 28 and 14 ohm parallel resistors in the second image? Is it because the current is also being split to the farleft 28 ohm resistor?)
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