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A student is asked to connect four cells of emf ε each and internal resistance r each in series (helping condition). By mistake he connects one cell in the opposite way. What will be the effective emf and effective internal resistance?

Asked in GSEB Board July 2018 · Combination of cells

• (1) 4ε, 2r
• (2) 2ε, 4r
• (3) 3ε, 2r
• (4) 4ε, 4r

Step-by-step solution

Why the other options are wrong

• (1) This keeps the emf at 4ε as if nothing were reversed, yet subtracts the reversed cell's internal resistance (3r - r = 2r). It is the other way round: a reversed cell subtracts its emf, while internal resistances always add.
• (3) 3ε treats the reversed cell as simply dropping out, and 2r subtracts its internal resistance (3r - r). The reversed cell's emf actively opposes the other three (3ε - ε = 2ε), and its r still carries the current, so the resistance is 4r.
• (4) 4ε, 4r is the result for the intended, correct connection. With one cell reversed the emf becomes 3ε - ε = 2ε; only the internal resistance stays 4r.

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