For the loop picture below, v1 = -2 V, v2 = -3 V and v3 = 0 V. Find vx in Volts.

Question

BlackTom AI · Accepted Answer

Kirchhoff’s Voltage Law (KVL) requires the algebraic sum of voltage rises and drops around any closed loop to equal zero. Relevant concepts: sign of each voltage depends on the terminal you traverse first (going from − to + is a rise +V, from + to − is a drop −V).

Step-by-step traversal and sign choices:
1. Choose clockwise around the loop. Start at the top-left node and move across the top element v2 from left to right. The top element labels left terminal as − and right as +, so traversing left→right is a rise: +v2.
2. Continue down the right vertical element (vx) from top to bottom. The right vertical is labeled + at the top, − at the bottom, so top→bottom is a drop: −vx.
3. Move across the bottom element v3 from right to left. The bottom block is labeled + on the right and − on the left, so right→left is a drop: −v3.
4. Move up the left vertical element v1 from bottom to top. The left vertical is labeled − at the bottom and + at the top, so bottom→top is a rise: +v1.

Write KVL sum = 0:
v2 − vx − v3 + v1 = 0

Rearrange to solve for vx:
−vx = −v1 − v2 + v3  (or better: move vx to right)
vx = v1 + v2 − v3

Plug in the given numerical values:
v1 = −2 V, v2 = −3 V, v3 = 0 V
vx = (−2) + (−3) − 0 = −5 V

Why the sign matters: a common mistake is to ignore terminal polarities (which would give +5 V) or to traverse elements in the opposite direction without flipping signs (which yields other incorrect values). The correct value, following KVL with the labeled polarities, is vx = −5 V, which matches the provided answer.

For the loop picture below, v1 = -2 V, v2 = -3 V and v3 = 0 V. Find vx in Volts.数值题

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