Nodal analysis and Mesh analysis

 What is meant by nodal analysis?

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

What is the purpose of nodal analysis?

The aim of nodal analysis is to determine the voltage at each node relative to the reference node (or ground).

Steps for Nodal Analysis

1. Identify all nodes.
2. Choose a reference node. Identify it with reference (ground) symbol. ...
3. Assign voltage variables to the other nodes (these are node voltages.)
4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 1

Find the voltage at each node

Solution

1. Identify all nodes
2. Choose a reference node. Identify it with reference (ground) symbol
3. Assign voltage variables to the other nodes (these are node voltages.)
4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 2                              

Find the voltage at each node

 

Solution

1. Identify all nodes
2. Choose a reference node. Identify it with reference (ground) symbol
3. Assign voltage variables to the other nodes (these are node voltages.)

4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 3

Find all the voltages

As Va = 10v and Vc = 20v , Vb can be easily found by

Mesh Current Analysis

Mesh Current Analysis is a technique used to find the currents circulating around a loop or mesh with in any closed path of a circuit.

Procedure of Mesh Analysis

• Step 1 − Identify the meshes and label the mesh currents in either clockwise or anti-clockwise direction.
• Step 2 − Observe the amount of current that flows through each element in terms of mesh currents.
• Step 3 − Write mesh equations to all meshes. Mesh equation is obtained by applying KVL first and then Ohm’s law.
• Step 4 − Solve the mesh equations obtained in Step 3 in order to get the mesh currents.

Example

Find the currents flowing in the resistor using Mesh Analysis

 

Solution

 

 

What is the difference between mesh analysis and nodal analysis?

• This method differs from the nodal method by using mesh currents instead of nodal voltages as circuit variables.
• Nodal method uses Kirchhoff's currents Law to consider nodal voltages, and Mesh method uses Kirchhoff's voltages Law to consider mesh currents. 
• Mesh is a loop, which does not contain any other loops