What is Thevenin’s theorem?

What is Thevenin’s theorem? 

Thevenin’s theorem provides a method for simplifying a circuit to a standard equivalent
form. This theorem can be used to simplify the analysis of complex circuits.
Statement:
Any linear bilateral network may be reduced to a simplified two-terminal circuit
consisting of a single voltage source (Vth) in series with a single resistor (Rth)
Procedure:
i) Remove the load resistance RL and put an open circuit across terminals.
ii) Find the voltage across open circuited terminals (Vth or Voc)
iii) Find the equivalent resistance Rth as seen from open circuited terminals by replacing
the voltage source by its internal resistance.
iv) Draw the thevenin’s equivalent circuit by a voltage Vth in series with the equivalent
resistance Rth

Find the current through RL by applying ohms law.
Explanation:
            Vth
IL = ----------------
        Rth + RL

Step 1: Open Circuit the Load Resistor (RL)

Step 2: Find Open Circuit Voltage (Vth)
Vth = P.D across terminals A
and B P.D across terminals A and B = P.D across R2 Resistor
                                        Vth = I x R2
                                             E
                                     I = ------------
                                        (R1 + R2)

                E. R2

       Vth = ------------------------

                     (R1 + R2) 

Step 3: Find Thevenin’s equivalent Resistance: Rth
                             
                                     R1 x R2
                           R12 =---------------
                                     R1 + R2
               
                            Rth = R12 + R3

Step 4: Draw Thevenin’s equivalent circuit

Step 5: Find the Load Current (IL):

                                       Vth
                             IL =--------------
                                    Rth + RL