# Confused about KCL & Nodal Analysis (basic stuff...)

by Nat3
Tags: analysis, basic, confused, nodal
 P: 393 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" $$I_{in} = I_{out}$$ 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: $$\frac{V_o - V_1}{1}$$ 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.