What is Nodal Analysis?
Nodal analysis is used for solving any electrical network, and it is defined as
The mathematical method for calculating the voltage distribution between the circuit nodes.
This method is also known as the node-voltage method since the node voltages are with respect to the ground. The following are the three laws that define the equation related to the voltage that is measured between each circuit node:
- Ohm’s law
- Kirchhoff’s voltage law
- Kirchhoff’s current law
| Table of Contents |
Features of Nodal Analysis
- Nodal analysis is an application of Kirchhoff’s current law.
- When there are ‘n’ nodes in a given electrical circuit, there will be ‘n-1’ simultaneous equations to be solved.
- To obtain all the node voltages, ‘n-1’ should be solved.
- The number of non-reference nodes and the number of nodal equations obtained are equal.
Recommended Video:
Procedure of Nodal Analysis
The following steps are to be followed while solving any electrical circuit using nodal analysis:
Step 1:
To identify the principal nodes and select one of them as a reference node. This reference node will be treated as the ground.
Step 2:
All the node voltages with respect to the ground from all the principal nodes should be labelled except the reference node.
Step 3:
The nodal equations at all the principal nodes except the reference node should have a nodal equation. The nodal equation is obtained from Kirchhoff’s current law and then from Ohm’s law.
Step 4:
To obtain the node voltages, the nodal equations can be determined by following Step 3.
Hence, for a given electrical circuit, the current flowing through any element and the voltage across any element can be determined using the node voltages.
Types of Nodes in Nodal Analysis
There are two types of nodes in nodal analysis:
- Non-reference node
- Reference node
Non-Reference Node
The node with a definite node voltage is a non-reference node.
Reference Node
The node that acts as a reference point to all the other nodes is known as the reference node, which is also known as the datum node.
There are two types of reference nodes, and they are:
- Chassis ground
A reference node that acts as a common node for more than one circuit is called chassis ground.
- Earth ground
In any circuit where the earth’s potential is used as a reference, it is known as the earth’s ground.
What is a Super Node?
The super node is defined as a voltage source connected between the two non-reference nodes such that these two nodes form a generalized node.
Properties of Super Node
The following are the properties of super nodes:
- The difference between the voltage of two non-reference nodes can be determined at the super node.
- A super node does not have its own voltage.
- Kirchhoff’s current law and Kirchhoff’s voltage law are both applied for solving the super node.
Nodal Analysis Examples
Example 1:
For the following circuit, find Va by nodal analysis.
Solution:
Step 1: To select a reference node and label the node voltages
Step 2: Apply Kirchhoff’s current law to all the nodes
Node 1:
Node 2:
Node 3:
From eq.1,2,3 we know that
V1 = 37v
V2 = 12v
V3 = 41
Step 3: To find the required quantities
Applying Kirchhoff’s voltage law in the above loop, we get
-V1 – Va + V2 = 0
Va = -25v
Example 2:
Determine the voltage at each node of the given circuit using nodal analysis.
Solution:
The number of nodes that are present in the given circuit is 3
The nodes that are present in the circuit are numbered as shown in the figure
Let node 2 be the reference node, and this node’s voltage will be zero.
Using Kirchhoff’s current law at each node, we get
This is a result of KCL at node 1
This is a result of KCL at node 3
Solving the above equations we get
V1 = 68.2v
V3 = 27.3v
Frequently Asked Questions – FAQs
If there are 12 nodes in a circuit, how many equations do we get?
We know that one node is always considered a reference node, so the number of equations we can get will always be less than the given number of nodes. As a result, the number of equations that may be derived here is 11.
Which law is used in nodal analysis?
Kirchhoff’s current law is used in nodal analysis.
What does Kirchhoff’s voltage law state?
According to Kirchhoff’s voltage law, the algebraic sum of the potential difference in any loop should equal zero.
What does Kirchhoff’s current law state?
According to Kirchhoff’s current law, the current flowing into a node should equal the current flowing out of it.
What is the advantage of nodal analysis?
The benefits of nodal analysis include the reduced number of equations necessary to determine unknown values
Stay tuned with BYJU’S to learn more about other Physics related topics.
Put your understanding of this concept to test by answering a few MCQs. Click Start Quiz to begin!
Select the correct answer and click on the "Finish" button
Check your score and explanations at the end of the quiz
Visit BYJU'S for all Physics related queries and study materials
Your result is as below
Comments