Nodal Analysis


Nodal analysis

Now we describe the procedure OF NODAL ANALYSIS and also we will solve some problems based on it.

 KCL or Kirchhoff's Current Law is used to find a current around a node and based on the principle of conservation of electric charge implies that:
Around a node or junction the algebraic sum of incoming and outgoing current is zero.





ALGORITHM
Followings are steps to perform numerical based on Nodal analysis .
1)    We have to count all nodes and loops.
2)    Now take a node (principle node) and find branch current around that node.
3)    We have to convert voltage and resistance of the branch into current i.e. apply ohms law







4)    Now consider that current, is following outward from that node (principal node).
5)    Current flows from high voltage to low voltage.
6)    Now take inward current as negative and outward current as a positive and write equation with inward current direction  towards the principal node as a negative before equals to (=) and vice versa for outwards current.
7)    Current in a battery go from (-) negative to (+) positive side.
8)  

      i.e. algebraic sum is zero and solve the equation(s) 



Now executes some numerical to clear the concept more firmly.

ILLUSTRATION 1:
Find branch current


Consider y as a principal node
Now apply KCL at y

IX + IY + (-IZ) + 10 + (-2) = 0

Let at “y” V volt exist, than find out all branch current by ohms law.









By solving above v =-8.42
Current at x y z branches are -1.684, 4.21,-2.1 units

ILLUSTRATION 2: find voltage around current source.


Solution: Know follow the steps

Here in the fig

Loops = 3

Nodes = 4
We convert that circuit into simpler circuit by combining 8 and 2 ohm resistance

Take branch current around node “a”

I1 + I2 – 2 = 0

As current flows from higher to lower voltage  assume voltage at a is higher.




By solving this we get
                                             45\6 volt

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