# Back To School – Let’s Calculate Current I3

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## 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…

For start, let’s try to remember two Kirchhoff’s Laws //
Kirchhoff’s Current Law – The algebraic sum of currents at a node is zero.
Kirchhoff’s Voltage Law – The algebraic sum of voltages around a closed circuit loop is zero.

– 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 UTh at nodes A and B can be easily calculated by disconnecting the right part of the circuit:

Thévenin’s equivalent resistance RTh 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):

Readers should note that UAB0 ≠ UAB:

UAB = UTh – RTh · I3 = 8.333 – 4.166 · 0.041 = 8.163

Comparing the three methods, we can conclude that Thévenin’s theorem is very powerful, in particular when a single current value is needed.

### Thevenin’s Theorem. Example with solution (VIDEO)

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