# Circuit with dependent source confusion

Can we find the value of $$\i'\$$ in this circuit, considering $$\I\$$ and $$\R\$$ are known?

Using Kirchhoff’s Current Law we have that $$\I = i + i'\$$.

If the dependent source voltage was $$\ki \;, \; k \neq R \$$ then from Kirchhoff’s Voltage Law we would have $$\(k-R)i=0\$$, and since $$\ k \neq R \$$ we have that $$\i=0\$$, so $$\i'=I\$$.

What happens when $$\ k=R \$$, as in the picture above? Kirchhoff's laws are theoretically satisfied for every value of $$\i\$$. Should we assume that $$\i\$$ is zero again? Or better, does $$\i'\$$ and by extension $$\i\$$ have a fixed value?

If $$\k = R\$$ then the voltage across the dependent source is $$\Ri\$$. The voltage across the resistor is equal to $$\Ri\$$. You are correct that KVL and KCL will be satisfied for all values of $$\i\$$, but that does not mean that you can assume $$\i = 0\$$.
I think you are being asked to think about the value of $$\i'\$$ as a function of $$\i\$$, not as an absolute value. You are almost there.
• So, can $i$ and $i'$ in this circuit take an infinite set of values, with the restriction that they satisfy $I = i+i'$ ? Can't we circuitally conclude, that since the dependent source branch has no resistance, then only this branch draws current from the current source, so $i=0$ ? – ggrin Mar 19 at 17:16
• An ideal voltage source never has resistance, and it doesn't matter. The only thing we know about a voltage source is that it constrains the voltage between its terminals. The voltage source can have a voltage across it even if it has no resistance. Therefore, there can be a voltage across the resistor, and a current through the resistor, and a current through the dependent source. No, you cannot conclude that $i=0$. – Elliot Alderson Mar 20 at 0:41