Nodal Analysis

In electric circuits’ analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents. Nodal Analysis provides a general procedure for analyzing circuits using node voltages as the circuit variables. 

Steps to Determine Node Voltages:

1. Select a node as the reference node, Assign voltages v1, v2, . . . . . , 

vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node.

2.Apply KCL to each of the n-1 non-reference nodes. Use Ohm’s law to express currents in terms of node voltages.

3. Solve the resulting simultaneous equations to obtain the unknown node voltages.

Nodal Analysis with Voltage Sources

Case 1: If the voltage source (dependent or independent) is connected between two non-reference nodes, the two non-reference nodes form a generalized node or super node, we apply both KCL and KVL to determine the node voltages.

Case 2: if a voltage source is connected between the reference node and a non-reference node, we simply set the voltage at the non-reference node equal to the voltage of the voltage source in figure 2 for example,

v₁ = 20V

What is supernode?

A supernode is formed by enclosing a (dependent or independent) voltage source connected between two non-reference nodes and any elements connected in parallel with it.

In figure 2 node 2 and node 3 form a supernode. Applying KCL at super node which are node 2 and 3 we get,

i1 + i4  = i2 + i3

To apply KVL redrawing the figure 2 circuit to figure 3 and going around the loop in the clockwise direction gives,

– v2 + 10 + v3 = 0

  Or  v2 – v3 = 10      ————————— (ii)

Overview of the Lesson :

In this lesson we tackled about the Methods of Analysis which is the Nodal Analysis. In nodal analysis, we are interested in finding the node voltages. Given a circuit with n nodes without voltage source. There are also ways in solving the node voltages; The shortcut method or the long method. The shortcut method is you can determine the equations of each node by determining the adjacent of the resistors and in the long method you can determine the equations by using Ohm’s law and Substitution method.

*Take note that; To use Crammers rule, you must derive the equation into matrix form.

This week is very stressful because we already know our scores in the 1^st prelim exam and it was very disappointing. Having low scores in exam, but I hope I can pass the 1^st prelim for bullet for the upcoming midterm and especially the finals.