Need help understanding Thévenin’s Theorem

[rstofer]

Let's look at the voltage first - this implies there is no load because we want the open circuit voltage

The current through the voltage divider is I = Vin / (R1 + R2) and the output voltage is I * R2 which results in (Vin * R2) / (R1 + R2)
There are other ways to solve the voltage divider, I decided to get pedantic about the loop current.

Looking back into the source with Vin shorted, all we have is R1 & R2 in parallel so the Thevenin Equivalent Resistance is (R1*R2)/(R1+R2)

So, our Thevenin Equivalent Circuit is:  Vth = (Vin * R2) / (R1 + R2) in series with a resistor Rth = (R1*R2)/(R1+R2)


The open circuit voltage is just what you see when you measure across R2 with no load connected.  The Thevenin resistance is, in this case, just the parallel combination of R1 and R2.


ADD:

Pretend Vin is 10V and R1 = R2 = 1 Ohm.  It's fairly obvious that the Thevenin voltage is 5V
Then calculate the Thevenin resistance as 0.5 Ohm.

Your equivalent circuit is a 5V source with a 0.5 Ohm series resistor.  Your maximum current is 10 Amps (5V / 0.5 Ohm), your open circuit voltage is 5V.  If you go back to the original circuit and short out R2, the maximum current is 10V / 1 Ohm = 10 Amps.  Same maximum current and same open circuit output voltage - 5V.  Circuits are equivalent.