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Hey, I am studying dependent sources.as an exercise i am trying to solve the circuit in the image. i have been banging my head against the wall on this problem and i really want some help. please. I tried node analysis always ending up with one more unknown than the number of equations.

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First, you can drop the two left 3000Ω resistors as they are in series with a current source — they don't make a difference to the rest of the circuit.

After that, you can easily see \$i_A\$ is always 1mA higher than the current supplied by the voltage source (mind the polarity!). So you can drop the 1mA current source and keep that in mind.

Third, the current supplied into \$i_A\$ by the voltage source is \$\frac{-3000 Ω\cdot i_A}{6000 Ω}=-\frac{1}{2}\cdot i_A\$

So, the whole formula reads

$$i_A=1\mathrm{mA}-\frac{1}{2}\cdot i_A$$

$$\frac{3}{2} \cdot i_A=1\mathrm{mA}$$

$$i_A=\frac{2}{3}\mathrm{mA}$$

$$U=\frac{2}{3}\mathrm{mA}\cdot3000Ω=2V$$

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first of all in the future post your attempt to the question.

I suspect where you are going wrong is not treating the points either side of the short as a single node, that is write a single KCL equation that takes into account all the current entering and leaving that node. That should give you an equation relating Ia and the voltage at that node.

From there, you can find an equation for the voltage at that node. Apologies if this part is actually what you are stuck on.

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