# Combinations of Cells

> Cell combinations for NEET Physics: series, parallel and mixed grouping, equivalent emf and internal resistance, max power transfer condition.

- Canonical URL: https://prepelephant.com/topics/neet-ug/physics/cell-combinations-neet
- Exam / course: NEET-UG · Subject: Physics
- Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team
- First published: 2026-10-02
- Last updated: 2026-10-02
- How to cite: "Combinations of Cells", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/cell-combinations-neet

## Direct answer

n identical cells of emf ε and internal resistance r combine like batteries with rules worth stating precisely: in series, emf nε and internal resistance nr (voltages add, so this arrangement feeds high-resistance loads); in parallel, emf ε and internal resistance r/n (currents add, suiting low-resistance loads). The circuit current follows I = nε/(R + nr) for series and I = ε/(R + r/n) for parallel, and for m rows of n cells each (mixed grouping), I = nε/(R + nr/m), maximised when the external resistance equals the total internal resistance, R = nr/m — the maximum power transfer condition. Non-identical cells in parallel are handled by the general equivalent: ε_eq = (Σε_i/r_i)/(Σ1/r_i), the current-weighted mean of the emfs.

## What you must remember

- **Series pack:** emf = nε, internal resistance = nr; current I = nε/(R + nr); advantageous when R >> r.
- **Parallel pack:** emf = ε, internal resistance = r/n; current I = nε/(nR + r); advantageous when R << r.
- **Mixed grouping (m rows of n):** I = nε/(R + nr/m); maximum current when R = nr/m, i.e. total internal resistance equals external.
- **Matching rule:** series for high-resistance circuits (torch with several cells), parallel for low-resistance draws — and identical cells in parallel do not raise emf, only sustain larger current longer.
- **Maximum power theorem:** the load receives greatest power P = ε^2R/(R + r)^2 when R = r, delivering P_max = ε^2/4r; efficiency then is only 50 per cent — power versus efficiency is a conceptual favourite.
- **Terminal voltage:** V = ε − Ir while discharging, V = ε + Ir while being charged; a cell's emf is its open-circuit potential difference.
- **Non-identical parallel cells:** ε_eq = (ε_1r_2 + ε_2r_1)/(r_1 + r_2) for two cells — a weighted average, never the arithmetic mean.

## A worked grouping comparison

Four cells, each ε = 2 V and r = 0.5 Ω, feed a resistor R = 0.5 Ω. Series: I = nε/(R + nr) = 8/(0.5 + 2) = 3.2 A. Parallel: I = ε/(R + r/n) = 2/(0.5 + 0.125) = 3.2 A. Identical answers — and not by accident: setting the two expressions equal, the n in the numerator cancels against cross-multiplying, and the currents match exactly when R = r, which these numbers satisfy. The clean general rule: series wins when R > r, parallel wins when R < r, and at R = r the grouping does not matter. Swap the load to R = 10 Ω and series delivers 8/12 ≈ 0.67 A against parallel's 2/10.125 ≈ 0.20 A — a threefold victory for series; swap it to R = 0.1 Ω and parallel returns 2/0.225 ≈ 8.9 A while series manages only 8/2.1 ≈ 3.8 A. The lesson: when a question offers a choice of grouping, do not trust the reflex that "more emf is better"; compare nε/(R + nr) with ε/(R + r/n) using the actual R.

## Where students slip

The reflex error is assuming series is always better because emf adds; with a low-resistance load, most of a series pack's emf drops across its own internal resistance as heat. Second, the maximum power point is often quoted as maximum efficiency — at R = r the cell delivers only half its power to the load, the rest warming itself; the exam separates these deliberately. Third, in mixed-grouping questions, count carefully: "24 cells, 4 per row" means n = 4 in series and m = 6 rows in parallel, and swapping m and n in nr/m flips the answer. A final discipline point: terminal voltage V = ε − Ir shrinks as current grows, which is why a car battery reads about 12 V open-circuit but sags during cranking — a daily-life framing NEET has used.

## Frequently asked questions

### What are the equivalent emf and internal resistance of n cells in series?

Emf nε and internal resistance nr, giving current I = nε/(R + nr); this suits external resistances much larger than r.

### Why does connecting cells in parallel not increase the emf?

Identical parallel cells all maintain the same potential difference, so the emf stays ε while the internal resistances divide (r/n), allowing larger total current for low-resistance loads.

### When does a mixed grouping deliver maximum current?

When the external resistance equals the total internal resistance, R = nr/m for m rows of n cells — the matched condition underlying maximum power transfer.

### At what load resistance is the power delivered by a cell maximum, and what is that power?

At R = r, the power peaks at P_max = ε^2/4r, with exactly half the cell's output dissipated internally.

### What is the terminal voltage of a cell during discharge?

V = ε − Ir, less than the emf by the internal drop; when the cell is being charged, the terminal voltage exceeds ε by the same amount.