Thevenenâ€™s theorem states that any collection of voltage sources, current sources, and resistors is electrically equivalent to an ideal voltage source with a single equivalent resistor.

Steps of the analysis:

- Find equivalent resistor of the circuit by replacing load resistor with an open circuit and in the rest of the circuit replace voltage sources with short connection and current sources with open circuit and calculate equivalent resistance.
- Find voltage across open circuit.
- Return load resistance back to initial electric circuit and replace rest of the circuit with Thevenenâ€™s equivalent.

Thevenenâ€™s analysis reduces electric circuit down to a single resistance in series with a constant voltage source.

In the following example, current **I _{5} **is calculated by replacing rest of the circuit with Thevenenâ€™s equivalent.

First step is to find equivalent resistance of the rest of the circuit:

Thevenin equivalent resistance for given circuit is

**R _{T}=(R_{1}+R_{2})||R_{3}** i.e.

Next step is to find voltage across points A and B:

Voltage across A and B can be simply found by using superposition theorem. It is Thevenenâ€™s voltage.

Third step is to replace circuit with Thevenenâ€™s equivalent.

Current **I _{5} **can be easily calculated as:

With Thevenin’s theorem, electrical circuit analysis is simpler then analysis with Northons theorem, since only voltage across open connection should be found no need to calculate equivalent current.

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