## Techniques for solving DC circuits

Referring to the following circuit, calculate **direct current I _{3}**:

- Using Kirchhoff’s laws;
- Using nodal analysis;
- Applying Thévenin’s theorem at nodes
**A**and**B**.

### Ok, let’s dive into calculation…

**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 **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 E**):

_{1}is presentThe left side of the circuit can now be substituted by **its Thévenin equivalent**, in order to calculate **current I _{3}**:

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

Readers should note that **U _{AB0} ≠ U_{AB}**:

U_{AB} = U_{Th} – R_{Th} · I_{3} = 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.

### Another Kirchhoff’s Laws Worked Example (VIDEO)

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

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