Final Answer:
The Thévenin equivalent circuit at the terminals is a voltage source V_th in series with a resistor R_th.
Step-by-step explanation:
To find the Thévenin equivalent circuit, we need to determine the open-circuit voltage (V_th) and the equivalent resistance (R_th) at the terminals. First, open the terminals and calculate the voltage across them, which is V_th. In the open-circuit condition, no current flows through the terminals, and any voltage drop across the internal resistance is negligible.
Next, short the voltage sources and determine the equivalent resistance R_th looking into the terminals. This involves deactivating all independent sources (setting voltage sources to 0 and current sources to open circuits) and calculating the resistance seen from the terminals.
In summary, the Thévenin equivalent circuit comprises a voltage source V_th equal to the open-circuit voltage and a resistor R_th equal to the equivalent resistance with all independent sources deactivated. This representation allows for simplified analysis of the original circuit when connected to external loads. Thévenin equivalents are particularly useful in understanding the behavior of complex circuits and facilitating further analysis or design processes.