60-thevenen-theorem

Thevenen’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:

  1. 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.
  2. Find voltage across open circuit.
  3. Return load resistance back to initial electric circuit and replace rest of the circuit with Thevenen’s equivalent.

Thevenen’s analysis reduces electric circuit down to a single resistance in series with a constant voltage source.

In the following example, current I5 is calculated by replacing rest of the circuit with Thevenen’s equivalent.

norton

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

norton01

Thevenin equivalent resistance for given circuit is
RT=(R1+R2)||R3 i.e.

thevenen_eq_02

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

norton02

Voltage across A and B can be simply found by using superposition theorem. It is Thevenen’s voltage.

thevenen_eq_03

Third step is to replace circuit with Thevenen’s equivalent.

thevenen02

Current I5 can be easily calculated as:

thevenen_eq_04

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.

Calculate real 2X2 system

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