Two ideal voltage sources are connected in series but in opposing polarity. If the sources are rated 6 V and 9 V, what is the resulting total source voltage across the series pair?

Introduction / Context:When voltage sources are placed in series, their net effect depends on whether they aid or oppose each other. Understanding polarity and series addition is a foundational DC circuit skill.

Given Data / Assumptions:

• Two ideal sources: 6 V and 9 V.
• Series-opposing connection (polarities oppose).
• No internal resistance is considered for the sum.

Concept / Approach:For series aiding, voltages add. For series opposing, the net is the difference, with the sign of the larger source. Thus, V_total = |9 V − 6 V| = 3 V, with polarity of the 9 V source prevailing.

Step-by-Step Solution:

Verification / Alternative check:Kirchhoff’s Voltage Law around the loop confirms that opposing sources subtract, yielding 3 V across the pair.

Why Other Options Are Wrong:

Common Pitfalls:Ignoring polarity marks on schematics or assuming all series sources always add; they subtract when placed in opposition.

Final Answer:3 V.