Example Problem Of Nodal Analysis Or Node Voltage Method

Example Problem Of Nodal Analysis Or Node Voltage Method

It is also a method of finding voltage at each node (It is that point where two or more than two wire are connected). After finding each node voltage we can easily find out the value of each branch current in the given network.

Method Of Solving Nodal Analysis:-

Consider a circuit, as follows:-

Step 1^st:-Firstly we have to find out the total no. of nodes in the given circuit.

The total no. of nodes is two named ‘V_a’ & ‘V_b’. As shown in the figure below.

Step 2^nd:-After finding no. of nodes, grounded or earthed one of the node having the maximum no. of branches are connected to that node.

For the above circuit both the nodes have equal no. of branches connected. So, we can ground any of them. Earthed means “To make potential zero at that node”. Here, we ground node ‘b’. i.e, V_b=0

Step 3^rd:-Now, flows current in each branch as our convenient direction and applying KCL at the active nodes.

Applying KCL at active node V_a, we get:-

        I₁=I₂+I₃                 ·············· (1)

For finding the value of ‘I₁’ , ‘I₂’ & ‘I₃’ ,we have to apply KVL in each branches as same as in current direction.

For I₁:-

    V_b+V-I₁R₁=V_a

=»0+V-I₁R₁=V_a

=»V-V_a=I₁R₁

So,

 

 For I₂ :-

 

 For I₃ :-

 

Putting all the value of ‘I₁’ , ‘I₂’ & ‘I₃’ in equation (1), we get

  

After solving these eqn, we can easily find the value of ‘V_a’.

Now, putting the value of V_a in I_1, I₂ & I₃ we can easily find out the value of current & voltage in any of the resistance of the given network.

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