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# What is Nodal Analysis?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The method we use for solving the given electrical network / electric circuit or the method we use for analyzing the given electrical network / electric circuit is known as the Method of Analysis. The **Nodal Analysis** method is one of the most important methods among all the methods of analysis.

The nodal method of circuit analysis is based on KCL. In this article, get an overview of the Nodal analysis method and how to solve an electric circuit/network problem by using this method. Here, first, you will get to know what Nodal analysis is and then the procedure of this method.

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## What is Nodal Analysis?

Node is a point, just an interconnection of at least two branches. We can classify the nodes into two types, namely simple nodes and principal nodes. A node is said to be a simple node if it has just an interconnection of only two branches. Whereas the principal node is a node that has an interconnection of at least three branches.

The nodal analysis is based on the KCL or Kirchhoff’s Current Law. The nodal analysis can be applied for:

- Planar networks
- Non-planar networks

In the Nodal analysis method, we will analyze the voltages at the principal nodes of the given electric circuit/network. Hence, we can call this method the node voltage analysis or Nodal analysis.

### Types of Nodes in Nodal Analysis

There are two types of nodes in the nodal analysis method, which are listed below:

- Reference node
- Non-reference node

## Nodal Analysis Steps

We can easily solve most network theory problems using the Nodal Analysis method. Here, first, you will get to know that the Nodal analysis is based on which laws & then the method Nodal analysis is generally used to determine which electrical quantities, etc. Now, let’s see the steps for solving the given network in the Nodal Analysis method.

**Step 1:**Observe the number of principal nodes in the given circuit and consider one of them as the reference node. Generally, we will assume this node voltage as zero.**Step 2:**Assign the node voltages at each principal node (except the reference node) concerning the reference node voltage.**Step 3:**Write the nodal equation (KCL & Ohm’s law) at each principal node whose node voltage is unknown.**Step 4:**Get the node voltages by solving the above nodal equations. Using these node voltages, we can find any branch’s response (voltage or current) in the given circuit.

## Nodal Analysis Problems

**Question 1:** Find the current I of the following electric circuit using the Nodal analysis method.

**Answer: **

**Step 1:** In the given electric circuit, there are 3 principal nodes (1, 2, and 3). Among these, we can consider node 3 as a reference node.

**Step 2:** The ground voltages at nodes 1 and 2 concerning the ground are V_{1} and V_{2,} respectively.

**Step 3:** Nodal equation at node 1 is

-2+V_{1}/1 + (V_{1}– V_{2})/1 = 0

=> 2V_{1}– V_{2}=2 …(1)

The nodal equation at node 2 is

5 + V_{2}/1 + (V_{2}– V_{1})/1 = 0

=>V_{1}– 2V_{2} =5 …(2)

**Step 4:** By solving the equations (1) and (2), we will get V1=-13 Volts and V2=-83 Volts.

The current, I= (0-V_{1})/1 = -V_{1}=1/3 A. So, using the Nodal analysis method, we got the current I value as 1/3 A.

**Question 2:** Find the current I of the following electric circuit using the Nodal analysis method.

**Answer: **

**Step 1:** In the given electric circuit, there are 2 principal nodes (1 and 2). Among these, we can consider node 2 as the reference node.

**Step 2:** The voltage at node 1 concerning the ground is V_{1}.

**Step 3:** Nodal equation at node 1 is

(V_{1}-20)/10+(V_{1}-5)/10+V_{1}/20=0 …(1)

**Step 4:** Let’s simplify the equation (1)

=>2V_{1}-40+2V_{1}-10+V_{1}=0

=>5V_{1}-=50

=>V_{1}-=10 Volts

The current, I=V_{1}/20=10/20=0.5 A. So, using the Nodal analysis method, we got the current I value as 0.5 A.

In this article, we discussed the Nodal analysis method for DC circuits, then solved the problems on Nodal analysis for DC circuits. Similarly, we can apply the Nodal analysis method for AC circuits to solve the problems of Nodal analysis in AC circuits.