Series-opposing sources — when two voltage sources are series-opposing, should their voltages be added arithmetically to get the total? Evaluate this statement.

Introduction / Context:
Multiple sources in series combine according to their polarities. “Series-aiding” means voltages add; “series-opposing” means they subtract. This question checks whether you recognize that opposing sources reduce the net voltage instead of increasing it by addition.

Given Data / Assumptions:

• Two ideal voltage sources in series.
• Opposing polarity orientation (one source fights the other).
• Linear, lumped circuit model.

Concept / Approach:
The correct way to combine series sources is to take their algebraic sum with sign, not a blind arithmetic sum. If V1 and V2 are oriented so that one is a rise while the other is a drop in the same loop traversal, the net is V_net = V1 − V2 (magnitude per polarity). Only when the sources aid each other do they add: V_net = V1 + V2. Therefore, the statement “series-opposing sources are added” is wrong.

Step-by-Step Solution:

Verification / Alternative check:
Example: 12 V source opposing a 9 V source → net 3 V. A DMM across the pair confirms ~3 V with polarity set by the larger source orientation, matching algebraic summation, not addition.

Why Other Options Are Wrong:

• Correct: Contradicts basic source combination rules.
• Only if identical / Only for AC: Irrelevant; algebraic sum applies regardless of equality or AC/DC as long as phasor polarities are considered for AC.

Common Pitfalls:
Ignoring polarity arrows and simply summing magnitudes. Always mark polarities and signs before applying KVL.

Final Answer:
Incorrect — series-opposing sources subtract; use the algebraic sum with signs.