# Nodal Analysis

By Mona Kumari|Updated : May 6th, 2022

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

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. In this article, we discussed the problems of Nodal analysis as well.

## What is Nodal Analysis?

Node is a point, which is 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 which has an interconnection of at least three branches.

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 method or Nodal analysis in short.

## Procedure of Nodal Analysis

We can solve most of the network theory problems easily by 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 present 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) with respect to 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. By using these node voltages, we can find the response (voltage or current) of any branch present in the given circuit.

## Problems on Nodal Analysis

Question 1: Find the current, I of the following electric circuit by 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 voltages at node 1 and node 2 with respect to the ground are V1 and V2 respectively. Step 3: Nodal equation at node 1 is

-2+V1/1 + (V1- V2)/1 = 0

=> 2V1- V2=2    …(1)

The nodal equation at node 2 is

5 + V2/1 + (V2- V1)/1 = 0

=>V1- 2V2 =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-V1)/1 = -V1=1/3 A. So, by using the Nodal analysis method, we got the value of current I as 1/3 A.

Question 2: Find the current, I of the following electric circuit by 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 with respect to the ground is V1. Step 3: Nodal equation at node 1 is

(V1-20)/10+(V1-5)/10+V1/20=0   …(1)

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

=>2V1-40+2V1-10+V1=0

=>5V1-=50

=>V1-=10 Volts

The current, I=V1/20=10/20=0.5 A. So, by using the Nodal analysis method, we got the value of current I as 0.5 A.

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

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## FAQs

• Nodal equation is nothing but the combination of KCL and ohm’s law. At any node, we can write the KCL equation first and then use ohm’s law in that equation wherever required. This resultant equation is known as the nodal equation. So, we can directly write the nodal equation at any node by using KCL and ohm’s law together.

• In the Nodal analysis method, we will write the nodal equations to find the unknown node voltages. So, the minimum number of nodal equations required will be the same as that of the number of unknown node voltages.

• For the given electric circuit, if the number of nodal equations to be solved is less than that of the number of mesh equations to be solved, then we can prefer the Nodal analysis method compared to the Mesh analysis method.

• By using Nodal analysis, we can determine the node voltages first. And then by using these node voltages, we can calculate the response (voltage or current) of any element present in the given circuit.

• A network is said to be a planar network, if we can draw that network in two-dimensional plane without having any crossovers. Otherwise, it is said to be a non-planar network. We can apply the Nodal analysis for both planar and non-planar networks because for each node we can assign node voltage whether it is planar network or non-planar network. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com