# Resistance reduction and source transformation to find voltage

• gfd43tg
In summary, the conversation discusses using resistance reduction and source transformation to find Vx in a circuit with multiple resistors and a current source. The individual is able to solve the problem by realizing that the resistors in between the current source are in parallel and using this information to perform source transformation. The final solution is Vx = 8 V.
gfd43tg
Gold Member

## Homework Statement

Use resistance reduction and source transformation to find Vx in the circuit below. All resistance values are in ohms.

## The Attempt at a Solution

For this problem, I know I can combine the 16 Ω resistors, but where I'm having a little trouble is knowing how to do the source transformation if the current source is parallel to the 12 Ω and 6Ω resistor. I can combine all of the resistors on the left and right side, but it will leave me with a current source in parallel to two resistors

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If the current source is in parallel with the 12 Ω and 6Ω resistors, then that also means the 12 Ω and 6Ω resistors are in parallel with each other...

See if you can reduce the network of resistors as much as possible (leaving the "Vx" resistor alone, of course).

You should be able to combine the entire network on the left side of the current source with the 6Ω on the right.
Let us know when you've got it.

I was able to solve it, and got Vx = 8 V. The problem was that I was unaware that the resistors in between the current source were in parallel, so when doing a source transformation I thought which one should I do it with, but now I know.

, which I'm not sure how to handle.One approach to solving this problem would be to first use resistance reduction to simplify the circuit as much as possible. This will involve combining the 16 Ω resistors and the 12 Ω and 6 Ω resistors. Once you have simplified the circuit as much as possible, you can then use source transformation to convert the current source into a voltage source and a resistor in series. This will allow you to apply Ohm's law to find the voltage across the 12 Ω and 6 Ω resistors, which will in turn help you find Vx.

Another approach would be to directly apply source transformation to the circuit before using resistance reduction. In this case, you would convert the current source into a voltage source and a resistor in parallel with the 12 Ω and 6 Ω resistors. You can then use Kirchhoff's voltage law to find the voltage across this parallel combination, which will again help you find Vx.

Both approaches are valid and will lead to the same result. The key is to carefully apply resistance reduction and source transformation techniques in a step-by-step manner, simplifying the circuit as you go along until you are able to find Vx.