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Network Theory – Nodal and Mesh Analysis
1. Nodal Analysis
Nodal analysis method is basically sum of two laws.
2. Ohms’s law
In this method we will use KCL & Ohm’s law to calculate the node voltages in the circuits.
Node → any function where atleast 3 branches will meet is known as anode.
- Determine number of modes in circuit
- Assign the mode potential and assign ground
- Write the KCL at each node and form the equations.
- Solve the equation and get the solution.
2. Mesh Analysis
Mesh analysis is basically sum of two laws
- Ohms’s law
In this method we will use KVL and Ohm’s law to calculate mesh current in the circuits.
Any closed path in the network is known as the loop.
“Smallest close paths in the circuit are known as the mesh”.
“Mesh is the loop in the network which will not consist any loop inside it.”
“Every mesh is loop but not Vice-Versa”
Here I, II, III are mesh and loop also but IV is only loop not mesh because that is consisting three meshes inside it.
Identify meshes and assign the mesh current by any direction (clockwise or counter clockwise)
Assign passive sign conversion
Write KVL Equation in each mesh,
i=1mVi=0 [Algebric sum of all the voltage drop in any closed path must have to be few]
Get the mesh equations of each mesh and calculate all mesh current.
-V1+i1R1+i1R2-i2R2=0 [for mesh 'I']
i2R2-i1R2+R3i2+R4i2-R4i3=0 [for mesh 'II']
R4i3-R4i2+R5i3+V2=0 [for mesh 'III']
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