Series aiding/opposing sources (algebraic sum): Three DC sources of −1.2 V, +15 V, and −6 V are connected in series. What is the magnitude of the total resultant voltage?
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A7.8 V
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B10.2 V
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C22.2 V
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D1.3 V
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E9.6 V
Answer
Correct Answer: 7.8 V
Explanation
Introduction / Context:When DC sources are connected in series, their voltages add algebraically, taking polarity into account. Aiding sources add; opposing sources subtract. The final question often asks either for signed result or its magnitude. Here, the magnitude is requested.
Given Data / Assumptions:
- Three ideal sources: −1.2 V, +15 V, −6 V.
- Series connection so voltages sum.
- The question asks for magnitude only (absolute value).
Concept / Approach:Use algebraic addition: V_total = V1 + V2 + V3. After computing the signed total, take the absolute value to get the magnitude. Be careful with negative signs representing opposing polarities.
Step-by-Step Solution:
Sum signed voltages: V_total = −1.2 + 15 − 6.Compute: −1.2 + 15 = 13.8; 13.8 − 6 = 7.8 V.Magnitude: |7.8 V| = 7.8 V.Answer: 7.8 V.Verification / Alternative check:Think in terms of aiding/opposing: the +15 V aids; the −1.2 V and −6 V oppose, netting 15 − (1.2 + 6) = 15 − 7.2 = 7.8 V. Same result.
Why Other Options Are Wrong:10.2 V and 22.2 V come from incorrect addition/misplacing signs. 1.3 V is unrelated to the provided numbers. 9.6 V would be 15 − 5.4, which is not our opposing sum.
Common Pitfalls:Dropping a sign, or forgetting that the question asks for magnitude, not signed polarity.
Final Answer:7.8 V