# Nodal analysis with dependent voltage source

1. Dec 12, 2015

1. The problem statement, all variables and given/known data

In attached image. Just curious as to how their nodal analysis is correct.

2. Relevant equations

$I_{in} = I_{out}$

3. The attempt at a solution

Solution in image.

I am just not sure how they applied nodal analysis here to find that $I_s = \frac{12}{12} + \frac{12}{6} + \frac{12-8}{4}$. If I'm not mistaken, they are just finding V/R, correct? But isn't the voltage in ALL the resistors dependent in some way on both the 12 V source attached and also the dependent voltage source? Why does it seem like they only included the dependent voltage only on the 4-ohm resistor? Is their solution correct?

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2. Dec 12, 2015

### Staff: Mentor

Their solution is correct. If the applied independent source were changed to another value all the currents would be affected by the change, yet the resulting ratio of V/Is would turn out the same, yielding the same Rth.

Perhaps you have some doubt about how the node equation itself was written?

3. Dec 13, 2015

I guess I'm just not entirely understanding why the dependent voltage source is not considered in these equations for the other 2 resistors. Doesn't this voltage source affect the true voltage across the 6- and 12-ohm resistor, thus requiring this to be included when analyzing the current passing through these resistors? It seems to me that they are considering the voltage through the 6- and 12-ohm resistor to be simply 12 V, but that doesn't appear obvious to me since there is more than one voltage source in this entire circuit.

4. Dec 13, 2015

### Staff: Mentor

The dependent source is not connected to the node where the 6 and 12 Ohm resistors connect; The external source is. So the external source must set their currents. Nothing can alter the potential difference imposed by a fixed voltage source and in this case the 12 V source is wired directly across those resistors.

5. Dec 13, 2015