Direction of current for Kirchhoff's Current Law

[filerosfer]

Homework Statement

Find the power absorbed by each element in the single node pair circuit of the figure, and show that the sum is equal to zero.

Homework Equations

Kirchhoff's current law... in current = out current

The Attempt at a Solution

This is the solution.

I have the solution (see below). However I hope someone can help me understand how they chose the direction of current for Kirchhoff's current law. I can visualize the 8 amps turning right and going into the middle node. The 7 amps is clearly going into the node. However, I'm not sure about how they know what signs to use for the current through all the resistors.

I know at least one of the currents through the middle node must go out. I'm wondering if it has to do with the fact that they define the positive voltage at the middle. I'll just confuse myself if I keep guessing though.

Thanks for any help.

 

[LowlyPion]

Welcome to PF.

The method chosen to solve the problem relies on the conservation of charge into a node. What goes in must go out and vice versa.

So yes, they chose a Vx as +, and current flows + to - . But if you notice the current sources flow counter to the flow of the current through the resistors.

The power approach summation they provide as a check is based on the notion that power = V*I, and so carrying the sign of the current to the voltage, they assign negative power numbers to the active current sources. Not entirely intuitive given that power through resistors for instance result in I²R of heat, and that makes no distinction for direction.

 

[filerosfer]

Thanks

But if you notice the current sources flow counter to the flow of the current through the resistors.

That is what I am confused about. How do you know that the current through the resistors all contribute to current "out" of the middle node?

 

[Maxwellkid]

I must adamantly insist that students start taking a different approach when starting to set up problems with circuits. you ought to assign letters between junctions, capacitors, resistors, inductors, and bridges. you ought to begin thinking about circuits with the statement, the potential from A to B is _______ and so forth and NOT resistor 1 has this potential drop and on and on.

 

[LowlyPion]

That is what I am confused about. How do you know that the current through the resistors all contribute to current "out" of the middle node?

Conceptually it must be "out" because the current sources are "in". (see the arrows?)

You can't keep putting water in a pipe with no drain from all directions. There has to be a drain. Nature doesn't use RotoRooter. That's what the conservation of charges is all about. What goes in is what comes out.

 

[filerosfer]

Conceptually it must be "out" because the current sources are "in". (see the arrows?)

You can't keep putting water in a pipe with no drain from all directions. There has to be a drain. Nature doesn't use RotoRooter. That's what the conservation of charges is all about. What goes in is what comes out.

Ya, but you only need 1 "out". Like can you tell the current through the 6 ohm resistor contributes to the "out".

 

[LowlyPion]

Ya, but you only need 1 "out". Like can you tell the current through the 6 ohm resistor contributes to the "out".

I trust that you see from the topology that all of the elements are parallel to one another. So actually whichever current flows through one resistor it will flow similarly in the others.

This addresses the previous good suggestion to label the nodes and consider potential changes in terms of from node to node.

 

[davieddy]

I must adamantly insist that students start taking a different approach when starting to set up problems with circuits. you ought to assign letters between junctions, capacitors, resistors, inductors, and bridges. you ought to begin thinking about circuits with the statement, the potential from A to B is _______ and so forth and NOT resistor 1 has this potential drop and on and on.

I endorse this sentiment.
By talking about the potentials, not only does the meaning of "potential difference"
(e.g. V_A - V_B) become clear, but Kirchoff's "potential drops"
law is rendered redundant (satisfied trivially).

In this problem there are only two different potentials involved (and you can
call one of them zero without loss of generality).

 

[Dadface]

Provided that the Ist law and 2nd law are adhered to it makes no difference numerically if some current directions are marked incorrectly.If the object is to find what a current is then a minus sign shows that the current flows in the opposite direction to that shown on the diagram.