Nodal Analysis with Voltage source

Greetings our beloved instructor! At last the final topic for the midterm has come. Yet we know it is too early to celebrate because we still have a long way to go. But nevertheless we are quite relieved knowing our coverage for the exams.

Doing nodal analysis can be achieve in two ways, Kirchhoff's current law and Kirchhoff's voltage law. These laws has been discussed on our earlier topics so we assume that elaboration is of no significance anymore. Knowing such we can continue to nodal analysis with voltage source. Of course steps in doing nodal analysis are the following.

Steps in Nodal Analysis

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.

In nodal analysis with voltage source, we are presented with two cases;

Nodal Analysis with Voltage source Cases:

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.

Presented in this example.

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

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

Steps in calculating voltage drops on supernodes:

Step 1. Take off all voltage sources in super-nodes and apply KCL to super-nodes.

Step 2. Put voltage sources back to the nodes and apply KVL to relative loops.

As shown in this illustration:

Learning:

This week we have learned another nodal analysis but this time with a voltage source. It is quite similar to nodal analysis with current source,but nodal analysis with voltage source will have a supernode, which is a combination of two non-reference nodes connected to the same voltage source. And will have another solution by introducing KVL to the computation together with the KCL on the supernodes. Aside from those, nodal analysis with voltage source is similar to our last week's topic, nodal analysis with current source.
Doing and solving for the values (i.e. voltage drop and current) across a circuit is a lot of fun! We know these topics will help us push through our ever dearly loved careers. Though it is hard at first, we know we can achieve such if we put our utmost effort unto it. It has been said that if there is a will, there is and will always have a way.