Back To School – Let’s Calculate Current I3

Techniques for solving DC circuits

Referring to the following circuit, calculate direct current I₃:

1. Using Kirchhoff’s laws;
2. Using nodal analysis;
3. Applying Thévenin’s theorem at nodes A and B.

Ok, let’s dive into calculation…

– KCL stands for Kirchhoff’s Current Law
– KVL stands for Kirchhoff’s Voltage Law

The following equation can be written:

Substituting values, we obtain:

Finally,

Thévenin’s voltage U_Th at nodes A and B can be easily calculated by disconnecting the right part of the circuit:

Thévenin’s equivalent resistance R_Th is the resistance “seen” from nodes A and B, when all generators are deactivated (in our case, only E₁ is present):

The left side of the circuit can now be substituted by its Thévenin equivalent, in order to calculate current I₃:

This single-mesh circuit can be easily solved using KVL (Kirchhoff’s voltage law):

Another Kirchhoff’s Laws Worked Example (VIDEO)

Thevenin’s Theorem. Example with solution (VIDEO)

Reference // Fundamentals of electric power engineering – Ceraolo, Massimo, Davide Poli.