Using mesh current analysis find the voltage v across the 3o

Using mesh current analysis, find the voltage, v, across the 3-ohm resistor. Write the three mesh equations and find the currents and then calculate the voltage v.

Solution

We have 3 loops in the given networkVLLL

KVL in loop 1

I1+2 (I1-I2)+3 (I1-I3)=2

6I₁-2I₂-3I₃=2 ----1

KVL in loop

2(I₂-I₁)+2I₂+(I₂-I₃)=-1

-2I₁+5I₂-I₃=-1 -----2

KVL in loop 3

3(I₃-I₁)+(I₃-I₂)+I₃=0

-3I₁-I₂+5I₃=0 ------3

on solving above 3 equations we will get

I₁=0.522A

I₂= 0.075A

I₃=0.38

Now voltage across 3 ohm resistance is given by

V= 3 (I₁-I₃)

V= 3 (0.522-0.328)

V=0.582V