# Node Method vs Simple KVL and KCL Equations Difference

I am just quite confused when deriving some equations for this simple circuit. Using just KCL and KVL (loops in green) to the best of my understanding, I get the first set of equations.

• Firstly, are they valid?

• Secondly, when using the node voltage method, I get the second set of equations with the nodes in blue writing. I would like to know if they are equivalent or which set (if any) is correct, as I am unsure and they don't seem equivalent unless I am missing something?

• Unless you may only use your cell phone, please use a desktop computer and apply the schematic button available to you when editing. Draw the schematic using the tools, carefully use the available arrows (lower down the tools on the left) to show current flow, and for the mesh technique carefully label the arrows. For nodal, use the "balloons" available near the top left to label each node. You can also use this link to examine some ways to write equations here, as well.
– jonk
Commented May 28, 2020 at 15:42

Firstly, I believe you have a sign error in your second KCL equation (although I'm having a little trouble reading it, so I could be wrong).

Assuming your algebra is correct, surely the node voltage method is equivalent to KCL/KVL. Look at your node voltage equations: they're simply using Ohm's law to determine all the currents passing through each node, and then the equations you get correspond to identically those from just applying KCL (although they're written in terms of voltages and resistances as opposed to currents).

From experience, I'd say with the circuit you've shown here, Mesh Analysis would probably be a little more efficient than Node Voltage Analysis, since your circuit only has one super-node and a bunch of other nodes that can't be clustered.

Having said all that, Node Voltage Analysis and Mesh Analysis are simply systematic methods of applying KCL and KVL. They're basically algorithms that prescribe steps for analyzing arbitrary circuits.

• Hi, sorry why do you say that my second KCL is the wrong sign. I am not sure which direction current flows but I thought they I2 and I2bar would add up to equal I1. Sorry I am very new to this Commented May 28, 2020 at 14:29
• It might just be that I can't see some of the arrows properly. Which direction is $\overline{T}_2$ pointing? Commented May 28, 2020 at 14:41
• Sorry, I mean the direction of the I_2 with the bar on top of it Commented May 28, 2020 at 14:42
• I just made it point up into the node but that was just a guess. I have no idea which way it is meant to go. From what you can tell are my KVL equations correct? Commented May 28, 2020 at 14:44
• If it's pointing up to the node, then indeed its sign is wrong, it should be flipped. Remember, you want to make sure that all current flowing into a node flows out of the node. With regard to which direction it is "meant" to go, this is something that you'll figure out by solving the equations. If doesn't matter which direction you draw the arrow (assuming your signs are all right), because if you mess up a direction, the resulting current you get will just be negative (which implies it's flowing in the opposite direction). Commented May 28, 2020 at 15:58