## Techniques for solving DC circuits

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

- Using Kirchhoffās laws;
- Using nodal analysis;
- Applying TheĢveninās theorem at nodes
**A**and**B**.

### Ok, let’s dive into calculation…

**Kirchhoffās Current Law –**Ā The algebraic sum of currents at a node is zero.

**Kirchhoffās Voltage Law –**The algebraic sum of voltages around a closed circuit loop is zero.

**– KCL** stands for Kirchhoffās Current Law

**– KVL** stands for Kirchhoffās Voltage Law

The following equation can be written:

Substituting values, we obtain:

Finally,

TheĢveninās voltage **U _{Th} at nodes A and B** can be easily calculated by disconnecting the right part of the circuit:

TheĢveninās equivalent resistance **R _{Th}** is the resistance

**āseenā 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 TheĢvenin equivalent**, in order to calculate **currentĀ I _{3}**:

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

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

U_{AB} = U_{Th} – R_{Th}Ā Ā· I_{3} = 8.333 – 4.166 Ā·Ā 0.041 = **8.163**

Comparing the three methods, **we can conclude that TheĢveninās 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.

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