Question

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

The circuit has nodes X, Y, Z, and W. Between X and Y there is a 20 V ideal source (in parallel with a 10 k\(\Omega\) resistor directly connecting X and Y). Between Y and Z there is a 10 k\(\Omega\) resistor. Between Y and W there is a 2 k\(\Omega\) resistor. Between X and W there is an ideal 100 V source (no series resistor in this branch). Between Z and W there is an ideal 20 V source (no series resistor in this branch) and, separately, a 1 k\(\Omega\) resistor.

• A. V_TH = 100 V, R_TH = 10 k\(\Omega\)
• B. V_TH = 140 V, R_TH = 0 \(\Omega\)
• C. V_TH = 100 V, R_TH = 0 \(\Omega\)
• D. V_TH = 140 V, R_TH = 10 k\(\Omega\)

Hint:

Both Y and Z are pinned directly by chains of ideal voltage sources back to the reference node, so their potentials do not depend on any external load; find each node voltage first, then subtract.

Answer 1

The Correct Option is B

A useful way to check this is to notice, before doing any node-voltage algebra, that every path from Y or Z back to the reference node W passes only through ideal voltage sources, never through a resistor alone.

From Y, the only way back to W without crossing a resistor first is Y to X (ideal 20 V source) then X to W (ideal 100 V source). Both are ideal sources, so this path fixes $V_Y$ completely, with zero equivalent resistance along it.

From Z, the direct path to W is the ideal 20 V source between Z and W, again with zero resistance.

Since both terminal nodes of interest, Y and Z, are each rigidly fixed by an unbroken chain of ideal sources back to ground, their difference $V_Y-V_Z$ can never be perturbed by any external load connected across Y-Z, no matter how much current that load draws. This is exactly the condition for a zero Thevenin resistance: $R_{TH}=0\,\Omega$.

Now compute the fixed node voltages: $V_X=100$ V (from the X-W source), so $V_Y=V_X+20=120$ V (from the X-Y source). And $V_Z=-20$ V (from the Z-W source, oriented so that W is 20 V above Z).

The open-circuit voltage is:

\[ V_{TH}=V_Y-V_Z=120-(-20)=140\text{ V} \]

Combined with the zero-resistance argument above:

\[ \boxed{V_{TH}=140\text{ V},\ R_{TH}=0\ \Omega} \]