# Norton resistance: dependent sources problem

So imagine that I have a circuit that only contains a resistor in parallel with a dependent source of current. The resistor has a resistance of $$3 k\Omega$$ and a current I. The dependent source of current has a current of 2I. Now I want to know the Norton resistance of this circuit. The correct answer is $$1 k\Omega$$

However I'm not getting there.

My attempt

Because $$R_N = \frac{U_0}{I_{sc}}$$

I attempted to calculate both. However I'm getting to a voltage of 0V. I might be thinking incorrectly. What I'm thinking is that well the resistance and the source have the same voltage which is equal to the voltage I want to obtain. So $$U= RI$$

Considering my node

$$I + 2I = 0$$ so I = 0 and the U = 0. I might be assuming something wrong, if someone could please clarify me. Thanks!

• If the current source produces 2I and, half that current flows through a 3 kohm resistor, then the other half of the current flows through another 3 kohm resistor. – Andy aka Nov 9 '16 at 19:51
• I can't make sense of a circuit that only "contains a resistor in parallel with a dependent source of current" and where the dependent current source is $2\cdot I$. Assuming the observed current is the current in the resistor, the only two solutions are $I=0$ and $I=\infty$, so far as I can tell off-hand. – jonk Nov 9 '16 at 20:53
• Please add a schematic of your circuit to make your question clear. For example, you haven't said whether the dependent source and the controlling current are oriented in the same or opposite directions. – The Photon Nov 9 '16 at 21:29
• BTW 0/0 is undefined and hence compatible with "correct" 1kohm result. This is only not the way to get the result. – carloc Nov 9 '16 at 22:07