Series-opposing sources: If a 24 V battery and a 6 V battery are connected in series but opposing each other, what is the resulting total voltage across the pair?

Introduction / Context:When multiple sources are placed in series, their voltages add algebraically, taking polarity into account. In a series-opposing configuration, one source subtracts from the other. This knowledge is important in battery pack design and when analyzing multi-source circuits for net driving voltage.

Given Data / Assumptions:

• Source 1: 24 V.
• Source 2: 6 V.
• They are connected in series opposing (polarities opposed).

Concept / Approach:For series-aiding, voltages add; for series-opposing, the net is the difference between magnitudes if they are aligned head-to-head. The effective polarity follows the larger-magnitude source. Therefore, compute V_net = 24 V − 6 V = 18 V in the direction of the 24 V source.

Step-by-Step Solution:

Verification / Alternative check:Draw a quick polarity sketch: placing the 6 V reversed relative to the 24 V shows two opposing EMFs. KVL around the loop yields the same algebraic difference of 18 V.

Why Other Options Are Wrong:

• 30 V: That would be series aiding, not opposing.
• 24 V: Ignores the opposing 6 V source.
• 0 V: Only true if the magnitudes matched exactly (e.g., 12 V opposing 12 V).

Common Pitfalls:

• Failing to account for polarity, assuming all series sources add.
• Sign mistakes when writing KVL, which can flip the result.

Final Answer:18 V