Nodal Voltage Method (Nodal Analysis)

Nodal Voltage Method (Nodal Analysis)

Posted by Prabhat Jani on 09:17 in Basic, Basic Electrical Engg, Circuit, Circuit Analysis

In the nodal analysis method a reference node in the network is chosen. Then the unknown voltages at the other nodes are determined with respect to the reference node. After determining the node voltages, currents in all branches can be calculated. This method of circuit analysis is suitable where a network has a number of loops, and hence a large number of simultaneous equations are to be solved. The procedure for the node voltage method is explained through an example.

Example 1.For the circuit shown in Fig. 2.29 determine the voltages at nodes B and C and calculate the current through the 8 Ω resistor.

Figure 2.29

Solution:

We will take one reference node at zero potential. Generally the node at which maximum branches are meeting is taken as the reference node. Let R is the reference node as shown in Fig. 2.30. The reference node will be called ground node or zero potential node.

Figure 2.30

Points F, G, R, H, I are at zero reference potential. Let us now assign potential at all nodes with respect to the reference node. Let V_D, V_B, V_C, V_E are the potentials at points D, B, C, and E, respectively. Let us also assume unknown currents I_I, I₂, I₃, I₄, and I₅flowing through the branches.

Applying Ohm’s law currents I₁, I₂, I₃, I₄, and I₅ are expressed as

To find I₃, we assume potential at point k as V_K. We can write, V_K + 3 = V_B

Applying KCL at node B,

Solving eqs. (i) and (ii), we get

and current in 8 Ω resistor,

More problems using this method have been solved separately.