The Thévenin equivalent circuit for the circuit to the left of the terminals X and Y in the following circuit is:
A) A voltage source of 4 V with series resistance 25Ω
B) A voltage source of 4 V with series resistance 8Ω
C) A voltage source of 5 V with series resistance 25Ω
D) A voltage source of 5 V with series resistance 8Ω

Question

Quizplus · Accepted Answer

To find the Thévenin equivalent circuit, we need to first find the equivalent resistance of the circuit looking into terminals X and Y.

To do this, we can combine the 2Ω and 3Ω resistors in parallel to get:

1/R = 1/2 + 1/3 = 5/6

R = 6/5 Ω = 1.2 Ω

Next, we need to find the open circuit voltage between terminals X and Y. Since no current will flow through the circuit when there is an open circuit, we can simply find the voltage across the 4Ω resistor using voltage division:

V_oc = 20V * (4Ω / (2Ω + 4Ω)) = 8V

Now we can put the circuit back together with the Thévenin equivalent circuit, which consists of a voltage source with voltage V_oc in series with a resistor with resistance R. Thus, the Thévenin equivalent circuit for the circuit to the left of the terminals X and Y is:

Answer: B
 The Thévenin equivalent circuit for the given circuit is a voltage source of 4 V with series resistance 8Ω. This is found by calculating the open-circuit voltage across terminals X and Y, which is 8 V, and finding the equivalent resistance looking into those terminals, which is 1.2 Ω. The voltage source is then placed in series with this equivalent resistance to form the Thévenin equivalent circuit.

The Thévenin Equivalent Circuit for the Circuit to the Left