Example Solved Problem Based on Mesh Analysis Or Mesh Method

Example Solved Problem Based on Mesh Analysis Method

Question:-Find the current through 5Ω resistance in the given network by using Mesh Method?

Solution: - 

In the given network, a current source is given. So, we have to first convert it into voltage source.

After conversion, we have to identify the total no. of independent loops. Now, in our converted circuit there are three identical individual loops. After getting, total no. of individual loops we flows current in each loops in our convenient direction. As follow:-

Three individual current i₁, i₂, i₃ are taken in each loop within clockwise direction as shown in above fig.

For finding each loops current, we applied KVL in each loops. 

Applying KVL in loop 1^st:-

16-10i₁-6i₁-8i₁+6i₂+8i₃=0

-24 i₁+6i₂+8i₃=-16

24 i₁-6i₂-8i₃=16       ··················· (1)

Again, Applying KVL in loop 2^nd:-

-6i₂-9i₂-5i₂+6i₁+5i₃=0

6i₁-20i₂+5i₃=0           ·················· (2)

Now, in loop 3^rd:-

-5i₃-12i₃-8i₃+8i₁+5i₂=0

8i₁+5i₂-25i₃=0           ················ (3) 

 

On solving eqn (1), eqn (2) & eqn (3), we easily get the value of each loop current. 
i.e,

             i₁= 0.869A

             i₂= 0.348A

             i₃= 0.348A

So, current through 5Ω resistance is:-

             I_5Ω= i₃-i₂ =0.348-0.348 = 0A

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