How do I know that ##i_x = 0## ?

[link223]

Homework Statement

How do I know that $i_x = 0 ~ ?$ Is it because of the fact that resistor, source and dependent current source are in parallel? If that is not the reason, what is?

Thanks in advance.

Relevant Equations

Norton's theorem

I was first thinking that i_x is zero because the 4 ohms resistor can be ignored because it is parallel with a short circuit, but I assumed that only the resistance is zero whilst i_x flows through and that is what'd make the voltage across 4-ohms resistor to be zero.

 

[.Scott]

In figure 4.44(a), the voltage across the 4-ohm resistor is zero. Therefore, there is no current flowing through the 4-ohm resistor. The resistance of that 4-ohm resistor has not changed. It is simply short-circuited.

 

[link223]

Ahaaa got it, thank you!
Just to make sure, So when I have a short circuit parallel to a resistor, the resistor will basically always stay intact, whilst the current will be zero on the other hand.

I was kind of confused, because we say the 4-ohms resistor is short-circuited from which I derive that it acts as a short circuit i.e. current can freely run through that branch(/resistor) which is basically not the case at all.