The Thévénin Equivalent of a circuit consists of a Thévénin voltage source in series with a Thévénin resistor and is valid for any load. In AC circuits a Thévénin equivalent circuit is valid for a single frequency.
Original Circuit Prior to the Thévénin Equivalent
The Thévénin voltage is the open circuit voltage at the output. calculation is straightforward node or loop circuit analysis. Using loop analysis:
Voc: [8 * I1] + [(8+2+6) * I2] - [6 * I3] = 1 A
I2 = ½A ==> Voc = ½A * 6
Ω= 3 V = Vth
Calculate the Thévénin resistance from the open circuit voltage and the short circuit current
(set RL = 0 and solve for I3) using Ohm's Law.
Rth = Voc / Isc = 3 V / [(4/9) A] = 27 / 4 Ω = Rth