For the circuit shown, which one of the following options correctly identifies the Thevenin’s equivalent parameters between nodes Y and Z?

The correct answer is VTH = 100 V, RTH = 0 Ω.

Step-by-Step Explanation:

1. Node Voltage Analysis:

Let node W at the bottom of the circuit be selected as the reference ground node, so that:

$V_W=0\text{V}$

Based on the independent voltage sources shown in the circuit diagram, we can determine the potentials at the other nodes:

• Node X: An independent voltage source of $100\text{V}$ is connected between node X and the reference node W, with the positive terminal (+) at X and the negative terminal (-) at W. Therefore:

  $V_X=100\text{V}$

• Node Y: An independent voltage source of $20\text{V}$ is connected directly between node X and node Y, with the negative terminal (-) at X and the positive terminal (+) at Y. Therefore:

  $V_Y=V_X+20\text{V}=100\text{V}+20\text{V}=120\text{V}$

• Node Z: An independent voltage source of $20\text{V}$ is connected between node Z and the reference node W, with the positive terminal (+) at Z and the negative terminal (-) at W. Therefore:

  $V_Z=20\text{V}$

2. Finding the Thevenin Voltage ($V_{\text{TH}}$):

The Thevenin equivalent voltage ($V_{\text{TH}}$) between nodes Y and Z is the open-circuit voltage difference across these two terminals:

$V_{\text{TH}}=V_Y-V_Z$

Substituting the node voltages calculated above:

$V_{\text{TH}}=120\text{V}-20\text{V}=100\text{V}$

3. Finding the Thevenin Resistance ($R_{\text{TH}}$):

To find the Thevenin resistance ($R_{\text{TH}}$) looking into the terminals Y and Z, we deactivate all independent sources (replace all voltage sources with short circuits):

• Short-circuiting the $100\text{V}$ source connects node X directly to node W.
• Short-circuiting the top $20\text{V}$ source connects node Y directly to node X.
• Short-circuiting the bottom-right $20\text{V}$ source connects node Z directly to node W.

As a result, nodes Y, X, W, and Z are all short-circuited together, meaning they form one single electrical node. Because there is a direct short-circuit path of zero resistance connecting node Y to node Z, the equivalent resistance looking between them is:

$R_{\text{TH}}=0\text{Ω}$