Use Thévenin's theorem to determine .
To find the Thévenin equivalent, we break the circuit at the load as shown below.
So, our goal is to find an equivalent circuit that contains only an independent voltage source in series with a resistor, as shown in Fig. (1-26-3), in such a way that the current-voltage relationship at the load is not changed.
Now, we need to find and . is equal to the open circuit voltage shown in Fig. (1-26-2). The current of resistor is zero because one of its terminals is not connected to any element; therefore, current cannot pass through it. Since the current of resistor is zero, the voltage source, and resistors form a voltage divider circuit and the voltage across the resistor can be determined by the voltage devision rule. Please not that we are able to use the voltage devision rule here just because the current of the resistor is zero. You may ask that there is no reason to prove that the current of the resistor is zero in the original circuit shown in Fig. (1-26-1). That is correct. However, we are calculating for the circuit shown in Fig. (1-26-1) and this is a different circuit. The Thévenin theorem guarantees that , it is not saying that is the voltage across the load in the original circuit.
Since the current of the resistor is zero:
Now, we need to find . An easy way to find for circuits without dependent sources is to turn off independent sources and find the equivalent resistance seen from the port. Recall that voltage sources should be replace with short circuits and current sources with open circuits. Here, there is only a voltage source that should be replaced by short circuit as shown in Fig. (1-26-4).
It is trivial to see that the and resistors are connected in parallel and then wired in series to the resistor. Therefore,
Now that and are found, we can use the Thévenin equivalent circuit depicted in Fig. (1-26-3) to calculate in the original circuit shown in Fig. (1-26-1). The voltage devision rule can be used here to find . We have,