Thevenin's Theorem 

Thevenin's Theorem States that it is possible to simplify any circuit, no mattter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of linear is identical to that found in Superposition theorem, where all the underlying equation must be linear.

Thevenin's theorem is useful in analyzing power system and other circuits where one particular resistor  in the circuit ( called the load resistor) is subjected to change, and re construct the circuit with calculation depend on what method you are gonna use.

example:



In this example I decide to choose R2 as the LOAD resistance in the circuit.  We temporarily remove R2(load resistance) from the circuit and reducing what's left to an equivalent circuit composed of a single voltage source and series resitance. The load resistance can be reconnected to this Thevenins equivalent circuit and calculation carried out as if the whole network were nothing but a simple series circuit.

This should be the picture of a Thevenin's equivalent circuit

The Thevenin equivalent circuit, if correctly derived, will behave exactly the same as the original circuit formed by B1, R1, R3, and B2. In other words, the load resistor (R2) voltage and current should be exactly the same for the same value of load resistance in the two circuits. The load resistor R2 cannot “tell the difference” between the original network of B1, R1, R3, and B2, and the Thevenin equivalent circuit of EThevenin, and RThevenin, provided that the values for EThevenin and RThevenin have been calculated correctly.

The advantage in performing the “Thevenin conversion” to the simpler circuit, of course, is that it makes load voltage and load current so much easier to solve than in the original network. Calculating the equivalent Thevenin source voltage and series resistance is actually quite easy. First, the chosen load resistor is removed from the original circuit, replaced with a break (open circuit):

Next, the voltage between the two points where the load resistor determined. Use whatever analysis methods are at your disposal to do this. In this case, the orignal circuit with the load resistor removed is nothing more than a simple series circuit with the voltage Vth, and so we can also determine the voltage across the open load terminals by applying the OHM's law and KVL.

there are the results:



the voltage between the two load connection points can be figured from the voltage and one of the resistor's voltage drops, and come out to 11.2 V which is our thevenins voltage.



to find the Thevenins series resistance for our equivalent circuit, we need the original circuit, then we remove the power source (independent sources) which is the same method of superposition theorem
The voltage source will be SHORTED and current sources will be OPEN circuit. And then we can figure out the resistance from one load terminal to other.



with the load resistor (2Ω) attached between the connection points, we can determine voltage acroos it and current through it as though the whole network were nothing more than a simple series circuit:


in the example notice that the voltage and current of R2 (8V and 4A) are identical to other method of analysis. The voltage and current figures for the thevenin series resistance and the thevenin source(total) do not apply to any component in the original circuit. Thevenins theorem is only useful for determining what happens to a single resistor in a network: the load.

REFLECTION:
The Thevenin's theorem is a way to reduce a network to an equivalent circuit composed of a single voltage source (Vth),series resistance (Rth), and the series load.

In using the thevenins theorem :
-find thevenins source voltage by removing the load resistor from the original circuit and calculate the voltage across the open connection points where load is connected.
-find the thevenins resistance by removing all power sources in the original circuit by shorting voltage sources and current sources open circuit.
-analyze the voltage and current for the load resistor following the rules for series circuits.

the other case in using the thevenin theorem is a circuit the contains a DEPENDENT source. which our professor did not tackle yet.. thanks for reading :)