Mesh Analysis


Mesh analysis

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

KVL or Kirchhoff's voltage law is use to find voltage in around a loop and based on the principle of conservation of electric energy implies that:

In any closed loop or a mesh the algebraic sum of total voltage is always zero.

ALGORITHM
Followings are steps to perform numerical based on Mesh analysis.

1.    We have to count all nodes and loops.
2.    Now we have to circulate the current in each loop.
3.    Direction of current given in numerical, other choose any direction and only sign difference occur in our result.
4.    We have to convert current and resistance of the branch into voltage i.e. apply ohms law




5.    Current in a battery go from (-) negative to (+) positive side.

6.    Now consider that when current following from (-) negative to (+) positive side, the voltage is negative on that element and write voltage with negative sign on L.H.S of our equation. Vice versa when current follow from (+) positive to (-) negative.

7.     Follow the fundamental rule of KVL 
  
8.    Solve the equations(s) and find the loop current
Now executes some numerical to concrete the concept more firmly.


ILLUSTRATION1: Find loop current
 

SOLUTION
In the given problem current in 10V voltage source is from - to + and hence voltage will be negative on LHS.

In given problem you can see that in all resistors and 20V source, current is from + to – and will be positive on LHS.

Now combine equation
V = I*R

-10 + 20 + I*(10 + 5 + 15) = 0

Ans is -0.33 that is opposite to the given direction.

ILLUSTRATION2: find loop current I1 and I2


Solution

Follow the above rules

Current in 5 ohm resistance will be I1-I2 when loop 1 is consider and I2-

I1 in loop 2

Now follow the same rule as described above 

In loop 1

-10 + I1*10 + 5*(I1-I2) + I1*15 = 0

In loop 2

I2*4 + I2*6 + 5*(I2-I1) = 0

Solve the above equations and we get
I1 = .117 amp
I2 = .354 amp

Thank  You

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