When two cells of negligible internal resistances and equal e.m.f. denoted by E$_1$ and E$_2$ are connected in parallel, combined e.m.f. E is given by

Analyze the question: Two cells with negligible internal resistance and equal e.m.f. (E₁ = E₂) are connected in parallel. We need the combined e.m.f.

Concept:

• Cells in series (aiding): e.m.f.s add, so E = E₁ + E₂.
• Cells in parallel: the combined e.m.f. is the same as that of a single cell, provided the cells have equal e.m.f. The cells share the current, but the potential difference across the combination does not increase.

Solution:

1. Connecting the cells in parallel means their positive terminals are joined together and their negative terminals are joined together.
2. The potential difference between the common terminals is fixed by the e.m.f. of one cell, since the other has the same e.m.f.
3. Because the e.m.f.s are equal and the internal resistances are negligible, no current circulates between the cells, and the terminal p.d. is just E₁, which equals E₂.

So:

E = E₁ = E₂

Checking the other options:

• A: E₁ + E₂ applies to cells in series, not parallel.
• B: This has the form used for resistors or capacitors in certain arrangements, and it is not a rule for e.m.f.
• D: A ratio of e.m.f.s has no physical meaning here.

**Correct answer: C.

Tip: Parallel cells give the same voltage but a longer-lasting supply, because the current is shared. Series cells give a higher voltage. Remember it as "Series adds voltage, parallel adds lifespan."