Confused about KCL & Nodal Analysis (basic stuff )

In summary, the student is seeking help understanding how to use KCL in nodal analysis. They express confusion about the diagram showing current going up instead of down and how to set up the KCL equation. The expert responds by explaining that the direction of current can be defined in any way and offers a suggested nodal equation that follows the standard convention. They also clarify that there is no need to add negatives in the equation and to simply stick with the math.
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Homework Statement



I'm confused about how to use KCL when doing Nodal Analysis. Please consider the diagram below:

[PLAIN]http://img27.imageshack.us/img27/4900/20091019131641633915550.jpg

Homework Equations



My first point of confusion is that the diagram shows the current "4Ix" going up, but I thought current always went from higher voltage to lower voltage? (which would be down, in this case).

I also am very confused on how to setup the KCL equation, as you'll see in my attempt below..

The Attempt at a Solution



To use KCL, we assume that all of the currents are either entering or leaving the node and then add them up, right? Since one of the currents is already shown as entering, would it be logical to write my equation with them all entering? I tried to write the KCL equation like this:

[PLAIN]http://img651.imageshack.us/img651/6033/codecogseqn.gif

The first term is the current entering from the left, the second is term the current going up -- it's negative because it's entering through the negative sign (ohms law) -- and the third term is the current entering on the right, also negative for the same reason as before.

I know this is wrong, but I've spent hours trying to figure this out and am still totally confused. Please help me understand!
 
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  • #2
you can define the direction of current any way you want. when you solve the unknown, you may find the current is negative, indicating the actual current is flowing in the opposite direction as your guess.

as for your nodal equations, they are almost right except for when you seemingly randomly throw in negatives with the odd reason of "ohms law"

[tex]I_{in} = I_{out}[/tex]
this is because charge must be conserved. What flows into a node must flow out of the node.

It is a common standard to define current to leave toward any branch with a resistor in it and to define the current of a branch with a current source as the same direction as that source (after all, why not?)

so the nodal equation you seek to write out would have the foundation as such (in words, not numbers):
current entering the node from the current source = current leaving the node toward the 1 ohm resistor + current leaving the node toward the 5 ohm resistor

don't add any silly negatives! just stick with the math. Current approaches the positive terminal of a resistor. As an example, "current leaving the node toward the 1 ohm resistor" would be like this mathematically:
[tex]\frac{V_o - V_1}{1}[/tex]

It's worth nothing, also, you could also define all the currents as entering the node for the branches with resistors. You will have V1 - V0 in the numerator for the same example resistor instead of v0 - v1. That would be the equivalency of subtracting the once labeled "in" current onto the "out" side. And when you distribute the subtraction through (v0 - v1) you get (v1 - v0), so it is mathematically the same. It all goes back to my original point: you can define the directions any way you want.
 

FAQ: Confused about KCL & Nodal Analysis (basic stuff )

1. What is KCL (Kirchhoff's Current Law)?

KCL is a fundamental law in circuit analysis that states that the sum of all currents entering and exiting a node in a circuit must equal zero. This law is based on the principle of conservation of charge.

2. How is KCL applied in circuit analysis?

To apply KCL, you must first identify all the currents entering and exiting a node in a circuit. Then, you can use the KCL equation (sum of currents = 0) to solve for any unknown currents at the node.

3. What is nodal analysis?

Nodal analysis is a method for solving circuits that uses KCL to analyze the currents at different nodes in a circuit. It is used to determine the voltage and current at each node in a circuit.

4. How is nodal analysis different from other circuit analysis methods?

Nodal analysis is different from other methods because it focuses on analyzing the currents at the nodes in a circuit, rather than the currents flowing through individual components. It is a more systematic and efficient approach to solving complex circuits.

5. What are some tips for understanding and applying KCL and nodal analysis?

Practice is key when it comes to understanding and applying KCL and nodal analysis. It is also helpful to draw clear diagrams and label all the currents and nodes in a circuit. Additionally, breaking down a complex circuit into smaller parts can make the analysis easier.

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