Introductory Electrical Engineering With Math Explained in Accessible Language

20Nodal Analysis: Circuit Analysis

20.1 Introduction

In this chapter, we will examine a technique of circuit analysis called voltage node analysis or simply nodal analysis.

This technique can be used to find currents and voltages across a circuit by using a zero reference and a peculiar way to use Ohm's law.

20.2 Examples

20.2.1 Example 1

Consider the circuit shown in Figure 20.1, composed of several voltage sources and resistors. We want to find the voltage between points A and B and the several branch currents.

Figure 20.1 Nodal analysis.

20.2.1.1 Solution

First thing to do, according to the nodal analysis, is to choose a point to be the circuit's zero reference, that is, the ground point. We select point B and redraw the circuit to include a ground point, as shown in Figure 20.2.

Figure 20.2 Ground reference.

Now that we have a ground point, we can say that the voltages across points C and ground and across D and ground are equal to V₁ and V₂, or 80 and 20 V, respectively.

There is no rule to choose the ground reference point. It is advised to choose the point where the negative poles of more voltage/current sources are connected.

However, the voltage across A, which is between A and ground, is not immediately obvious. To find this voltage we must analyze the ...