Why do cells have internal resistance, and how does it affect their performance?

Cells have internal resistance due to the opposition offered by the electrolyte and electrodes to the flow of ions and electrons within the cell. This resistance causes a voltage drop ($Ir$) across the cell's internal components when current flows. Consequently, the terminal voltage available to the external circuit ($V = E - Ir$) is always less than the cell's EMF ($E$). A higher internal resistance means more energy is dissipated as heat inside the cell, reducing its efficiency and limiting the maximum current it can deliver. For example, old batteries often have increased internal resistance, leading to a significant drop in terminal voltage under load.

When is it more advantageous to connect cells in series, and when in parallel?

Connecting cells in series is advantageous when you need a higher total voltage. The EMFs add up, making it suitable for devices requiring a greater potential difference, like flashlights or certain electronic circuits. Parallel connection is beneficial when you need to deliver a larger total current or increase the battery's capacity (how long it can supply current) without increasing the voltage. It also effectively reduces the overall internal resistance of the combination, which is good for low-resistance loads. For optimal performance, parallel cells should ideally have identical EMFs to prevent internal current circulation.

What happens if cells with different EMFs are connected in parallel?

Connecting cells with different EMFs in parallel is generally not recommended. If their EMFs are not identical, a circulating current will flow internally between the cells, even without an external load. The cell with the higher EMF will discharge into the cell with the lower EMF. This leads to energy loss as heat, reduces the overall efficiency, and can potentially damage the cells. The equivalent EMF of such a combination is a weighted average, and the equivalent internal resistance is calculated using the reciprocal sum formula, but the internal current flow makes it inefficient.

Can internal resistance be ignored in circuit calculations?

Internal resistance can only be ignored if it is explicitly stated that the cells are 'ideal' or if the external resistance ($R$) is significantly larger than the total internal resistance ($r_{eq}$) of the cell combination ($R gg r_{eq}$). In such cases, the voltage drop across the internal resistance is negligible compared to the voltage drop across the external load. However, for most realistic scenarios and especially in NEET problems, internal resistance is a critical factor and must be included in calculations to accurately determine current, terminal voltage, and power.

What is the condition for maximum current from a cell combination?

The maximum current from a cell combination (series, parallel, or mixed) to an external load $R$ occurs when the external resistance $R$ is equal to the equivalent internal resistance ($r_{eq}$) of the cell combination. This is a specific case of the maximum power transfer theorem, which states that maximum power is delivered to the load when the load resistance equals the source resistance. While maximum power is delivered when $R = r_{eq}$, the maximum current is achieved when $R$ is as small as possible, ideally zero (short circuit). However, in practical terms, if we are looking for the maximum current *under a variable load*, the condition $R=r_{eq}$ is often discussed in the context of power transfer. For simply maximum current, $R$ should be minimized.

Why do internal resistances always add up in series, even if polarities are reversed?

Internal resistance is a scalar quantity representing the opposition to current flow within the cell, regardless of the direction of current or the cell's polarity. It's a measure of energy dissipation as heat. When cells are connected in series, the current has to pass through the internal resistance of each cell sequentially. Therefore, the total opposition to current flow from the internal components simply accumulates, meaning the internal resistances always add up arithmetically, irrespective of whether the EMFs are aiding or opposing each other. The polarity only affects the direction and magnitude of the net EMF, not the resistive property itself.

Cells in Series and Parallel

Physics

NEET UG

Version 1Updated 22 Mar 2026

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When multiple electrochemical cells are connected together, they form a battery or a cell combination. The manner in which these cells are interconnected significantly influences the overall electromotive force (EMF), the equivalent internal resistance, and consequently, the total current that can be delivered to an external circuit. The two fundamental configurations for connecting cells are seri…

Quick Summary

Understanding how to connect cells in series and parallel is crucial for NEET Physics. A cell is characterized by its Electromotive Force (EMF, $E$ ) and internal resistance ( $r$ ). When cells are connected in series, their EMFs add up (if aiding) or subtract (if opposing), and their internal resistances always add up.

This configuration is used to achieve a higher total voltage. The current drawn from $n$ identical cells in series to an external resistor $R$ is $I = \frac{nE}{R + nr}$ . For maximum current, series is beneficial when $R gg nr$ .

When cells are connected in parallel (ideally identical cells), the equivalent EMF remains the same as a single cell ( $E_{eq} = E$ ), but the equivalent internal resistance decreases ( $r_{eq} = \frac{r}{n}$ ).

This setup increases the current capacity and is beneficial when $R ll r/n$ . Mixed grouping combines series and parallel, offering flexibility to achieve desired voltage and current characteristics. For maximum current in a mixed group, the external resistance $R$ should match the equivalent internal resistance $r_{eq} = \frac{nr}{m}$ .

Always account for internal resistance in calculations.

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Key Concepts

Series Connection of Cells

In a series connection, cells are arranged sequentially, typically with the positive terminal of one cell…

Parallel Connection of Cells

In a parallel connection, all positive terminals of the cells are joined to a common point, and all negative…

Mixed Grouping of Cells

Mixed grouping involves arranging cells in both series and parallel configurations. A common setup is to have…

Series Connection: —

E_{eq} = \sum E_i

r_{eq} = \sum r_i

. Current

I = \frac{E_{eq}}{R + r_{eq}}

Parallel Connection (Identical Cells): —

E_{eq} = E

r_{eq} = r/n

. Current

I = \frac{E}{R + r/n}

Mixed Grouping ($m$ rows, $n$ cells/row): —

E_{eq} = nE

r_{eq} = nr/m

. Current

I = \frac{nE}{R + nr/m}

Maximum Current (Mixed Grouping): —

R = nr/m

Terminal Voltage: —

V = E - Ir

(discharging).

Internal Resistance ($r$): — Always adds in series, decreases in parallel.

S.V.A.P.C.I.R.

Series: Voltage Adds, Polarity matters for EMF, Current is same, Internal Resistance adds.

Parallel: Current Increases, Resistance decreases, Voltage is same (for identical cells), Internal Resistance divides.