Direction of current flow in KCL/Node Voltage Confusion

[Marcin H]

Homework Statement

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Homework Equations

V=IR
KCL/Node Voltage

The Attempt at a Solution

These are the solutions to some old homework assignments that my teacher posted, but I am very confused on the way he labeled his current flows in these problems. In the first picture he says that the current from the left branch is flowing into the node. In the second picture he is saying that all currents are flowing out of the nodes. The polaritites in both circuits are the same. Why is it that in the first picture we have current flowing into the node? That would mean current is flowing - to + which is not the conventional way of doing it. Does it have something to do with the dependent current source? Do we treat those differently? Also, why are the polarities on the resistor + to - from left to right?

It seems that in other homework problems it's the same. The source is always the same orientation + - top to bot but the current sometimes goes into the node and sometimes it goes out. HOW DO YOU CHOOSE?? WHAT IS CORRECT? If you choose wrong then your KCL will be different in both cases and you will get a wrong answer.

 

[cnh1995]

HOW DO YOU CHOOSE?? WHAT IS CORRECT?

You can choose ANY direction for the currents. If the chosen directions are not correct, you'll get negative values for the currents after solving KCL and KVL equations, which means actual direction is the opposite of chosen direction.

 

[Marcin H]

You can choose ANY direction for the currents. If the chosen directions are not correct, you'll get negative values for the currents after solving KCL and KVL equations, which means actual direction is the opposite of chosen direction.

In the second example I chose the left branch to have the current going out. So I had the same equation except with one part on the other side. So I had:

(Vx - 5)/3 = Vx/6 + 2x

I assumed that the current is going out for the left branch. Solving for Vx I got something weird like -11/10. The answer in the solutions is Vx = (2/3) V so I did not get the negative of that. I have had this problem several times. I heard that it doesn't matter what direction you choose, but it looks like it does. Why?

 

[NascentOxygen]

(Vx - 5)/3 = Vx/6 + 2x

You are using a rule "current out of branch 1 = currents out of all the other branches". We can call this this the Marcin H Rule because no one else has ever heard of it.

I'm positive that you'll have more success by using the much more trendy KCL instead. Here is one way to express it: Sum of all currents leaving a node = 0

An alternative but equivalent way to express KCL is: Sum of all currents entering a node = 0

A correct but all-too-easily-confused way is: Sum of the currents entering a node = sum of those currents leaving

 

[CWatters]

+1

I also find I make far fewer sign errors if I force myself to write the KVL/KVC equations in the form x + y + z = 0 and not x + y = -z