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?
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A3 V
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B16 V
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C7.5 V
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D8 V
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ENone of the above
Answer
Correct Answer: 3 V
Explanation
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:
1) Identify opposing polarities.2) Compute magnitude: 9 − 6 = 3.3) Assign polarity of the larger source if needed; magnitude is 3 V.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:
16 V: That is the series-aiding sum, not opposing.7.5 V or 8 V: Arbitrary averages; not based on polarity addition rules.None of the above: Incorrect because 3 V is correct.Common Pitfalls:Ignoring polarity marks on schematics or assuming all series sources always add; they subtract when placed in opposition.
Final Answer:3 V.