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Two batteries of emf ε₁ and ε₂ (ε₂ > ε₁) and internal resistances r₁ and r₂ respectively are connected in parallel as shown in the figure. Which of the following is correct?

Asked in GSEB Board March 2023 · Combination of cells

• (1) The equivalent emf is given by ε_eq = ε₁ + ε₂.
• (2) The equivalent emf ε_eq is smaller than ε₁.
• (3) The equivalent emf ε_eq of the two cells is between ε₁ and ε₂, i.e. ε₁ < ε_eq < ε₂.
• (4) ε_eq is independent of the internal resistances r₁ and r₂.

Step-by-step solution

Why the other options are wrong

• (1) Adding emfs is the rule for cells in series. In parallel both cells share the same two terminals, and the combined emf is a weighted average, not a sum.
• (2) ε_eq = (ε₁r₂ + ε₂r₁)/(r₁ + r₂) is an average of ε₁ and ε₂ with positive weights, so it can never fall below the smaller emf ε₁.
• (4) The weights in ε_eq = (ε₁r₂ + ε₂r₁)/(r₁ + r₂) are the internal resistances themselves; changing r₁ or r₂ moves ε_eq toward one cell or the other.

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