 The Laws of Circuit - you can learn and practice by just reading

Node Voltage Method

Why the 3 laws are not enough?
You learned about the most fundamental laws in electrical engineering: Ohm's Law, Kirchhoff's Current Law (KCL), and Kirchhoff's Voltage Law (KVL). You also learned about the Passive Convention in current flow direction, voltage polarity, and power calculation. And you guys, I hope, had a lot practice time to apply the above concepts, and could solve all the problems using only the laws and the convention.  There is no doubt that you can solve all circuit problems however complex or big they are.  Of course with a lot of practices. However, when there are a lot of variables involved in analysis, a direct application of the laws and the convention may cause some practical problems: too many equations to be solved. Apparently, we need some easier application of the Law for somewhat complex circuit problems.

KCL in Disguise
One of the "methods" we can apply is "a disguised KCL" at nodes.  This "KCL in disguise" is called "node voltage method."   In other words, Node voltage method is nothing but KCL.  However, there is a big difference.  In KCL, all the terms in your KCL equations are expressed in current; in Node voltage method, all the terms in the equations are expressed by a current equivalent, namely, Node voltage over Resistance, obtained by applying the Ohm's Law.  So instead of using current proper (unless there is a current source involved), we express the current by the voltage across over the resistance.  The "voltage across" must be expressed by the difference in node voltages in the nodal analysis.    All in all, I summarize it as:
* Node voltage method is actually "KCL in disguise."
* Node voltage method applies KCL at nodes.
* Instead of directly using the KCL in current form, we rephrase the currents (by applying Ohm's Law) in (voltage across) over (resistance) form.

Node Voltage vs. "Voltage Across"
Then, why do we use  'node voltage' instead of just 'voltage'?  It's all because of equation complexities and the desire to minimize the number of unknown variables.  By the way, voltage is a potential different between two points.  That's why we use the term 'voltage across' a resistor.  Node voltage is a voltage between a node referred and the designated reference node (like ground).

Node Method Application Order
Here is the order of node voltage method application:
a. Select an essential node as the reference node
b. Remember a “node voltage” is a voltage between a node and the reference node
c. Assign node voltages to the remaining essential nodes
d. At each of the nodes, express the branch currents in terms of node voltages (using Ohm’s Law)
e. Apply KCL to each node
f. Solve the resulting simultaneous equations to obtain the unknown node voltages.

WWW.MWFTR.COM