Final answer:
The Thevenin equivalent circuit for a portion of a larger circuit can be found by turning off all independent voltage sources to calculate equivalent resistance and by finding the open-circuit voltage, which together define the Thevenin voltage and resistance.
Step-by-step explanation:
To determine the Thevenin equivalent circuit for the portion of the circuit viewed by RL (1Ω), we need to follow these steps: First, turn off all independent voltage sources (set them to zero or replace them with a wire) and calculate the equivalent resistance seen from the terminals 'a' and 'b' where the load resistor RL is connected. Next, we calculate the Thevenin voltage, Vth, by finding the open-circuit voltage across 'a' and 'b' with the load resistor removed.
The equivalent resistance calculation involves combining resistors in series and parallel. For example, if there are two resistors R1 and R2 in parallel, we use the formula 1/Rtotal = 1/R1 + 1/R2 to find the equivalent resistance. If there are resistors R3 and R4 in series, their equivalent resistance is Req = R3 + R4. After combining all the resistors, we reinsert the reduced resistances into the circuit which gives us a simplified diagram to work with.
Finally, after calculating the Thevenin voltage and resistance, we have the Thevenin equivalent circuit which consists of a single voltage source Vth in series with a single resistor Rth.