For the loop picture below, v1 = 1 V, v2 = -1 V and v3 = 2 V. Find vx in Volts.

Question

BlackTom AI · Accepted Answer

Kirchhoff's Voltage Law (KVL) around the closed loop gives the sum of signed voltage changes = 0. Choose a clockwise traversal starting at the top-left junction and follow the labeled polarities on each element.

Relevant polarity labels (from the diagram):
- Top element v2: + on the left, − on the right.
- Right element vx: − at the top, + at the bottom.
- Bottom element v3: + on the left, − on the right.
- Left element v1: + at the top, − at the bottom.

Traverse clockwise and record the voltage change across each element in the order encountered:
1) Across the top (left → right) we go from + to − on v2, so the change = −v2.
2) Down the right element (top → bottom) we go from − to + on vx, so the change = +vx.
3) Across the bottom (right → left) we go from − to + on v3 (because v3 has + on left, − on right), so the change = +v3.
4) Up the left element (bottom → top) we go from − to + on v1, so the change = +v1.

KVL: (−v2) + vx + v3 + v1 = 0.

Solve for vx:
vx = v2 − v3 − v1.

Substitute the given numeric values (v1 = 1 V, v2 = −1 V, v3 = 2 V):
vx = (−1) − 2 − 1 = −4 V.

Why this is correct: the algebra follows directly from KVL and careful accounting of sign changes when moving from the labeled + terminal to − terminal (a drop) or from − to + (a rise). Common mistakes are sign errors (for example forgetting that v2 is −1 V or reversing traversal direction without adjusting signs), which would produce incorrect answers such as +4 V or −2 V.

Final answer confirmed: vx = −4 V (matches the provided answer).

For the loop picture below, v1 = 1 V, v2 = -1 V and v3 = 2 V. Find vx in Volts.Numerical

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