Thevenin's theorem and steps

Thevenin's theorem: any linear, bilateral two-terminal network containing independent sources and resistors can be replaced by an equivalent circuit consisting of a single voltage source Vth in series with a single resistance Rth, connected across the same two terminals. The load current is then I = Vth/(Rth + RL).

Steps to find Vth and Rth

1. Identify the load (or the two terminals of interest) and remove it from the circuit, leaving terminals a and b open.
2. To find Vth: calculate the open-circuit voltage between a and b using KVL, KCL, a voltage divider or nodal analysis.
3. To find Rth: set all independent sources to zero (replace voltage sources by short circuits and current sources by open circuits). Find the equivalent resistance seen looking into terminals a and b by series/parallel reduction.
4. Draw the Thevenin equivalent: Vth in series with Rth.
5. Reconnect the load RL and calculate I = Vth/(Rth + RL).

 (a) Original circuit            (b) Load removed: find Vth
     +-----------+ a                 +-----------+ a
     |  Linear   |-----+             |  Linear   |----o +
     |  network  |    [RL]           |  network  |      Vth = Voc
     |           |-----+             |           |----o -
     +-----------+ b                 +-----------+ b

 (c) Sources zeroed: find Rth    (d) Thevenin equivalent
     +-----------+ a                     Rth
     | V -> short|----o             +--/\/\/\--+ a
     | I -> open |      <-- Rth     |          |
     |           |----o            Vth       [RL]
     +-----------+ b                |          |
                                    +----------+ b

Rth can also be found as Vth/Isc, where Isc is the short-circuit current between a and b. If a dependent source is present, it is not set to zero; instead, apply a test source at the terminals and find Rth = Vtest/Itest.