Branch Current Analysis: Application of Branch Current Method in a 3 Loop Circuit

In our previous tutorial, we learned the application of Branch current analysis in a 2 loop circuit with an example.

In this example, a network having three loops is solved using branch current analysis.

Step 1: Let's first label the circuit:

Step 2: Apply the Kirchhoff's voltage law in the loop between I2 and I3.

5 V = 2 I ₂ - 2 I ₃ ...  (1)

Step 3: Apply KVL in the right loop.
1 V = 2 I ₃ + 2 I ₄ ...  (2)

Step 4: Apply Kirchhoff's current law at node a.
1 A  + I ₂ + I ₃ = I ₄ ... (3)

Solving the three equations we obtain our final answers:
I ₂ = 1.5 A
I ₃ = - 1 A
I ₄ = 1.5 A
Negative sign with current I ₃ indicates that actual current flow is opposite to our assumed direction of the current.