Internal Resistance of a Cell – Definition, Formula, Calculation

Every battery or electrical cell has some inherent resistance that limits the flow of current. This property is called the internal resistance of a cell. Understanding it is essential to analyze how efficiently a cell delivers power and why the terminal voltage drops when current flows through it.

Table of Contents

What is Internal Resistance of a Cell?

The internal resistance of a cell is the opposition offered by the electrolyte and electrodes inside the cell to the flow of electric current.

When current passes through the cell, part of the energy is lost due to this internal opposition. As a result, the terminal voltage becomes slightly less than the electromotive force (EMF) of the cell.

In simple terms, internal resistance is the resistance within the cell that causes a voltage drop when the cell supplies current.

Internal Resistance Formula

The relationship between EMF, terminal voltage, and internal resistance is given by:

Equation showing the relationship between EMF (E), terminal voltage (V), and internal resistance (r) of a cell: E = V + Ir

Where:

E = EMF of the cell (V)
V = Terminal voltage (V)
I= Current (A)
r = Internal resistance (Ω)

Rearranging gives the formula for internal resistance:

Formula for internal resistance of a cell showing r = (E − V) / I, where E is EMF, V is terminal voltage, and I is current.

This equation shows how internal resistance can be calculated using EMF, terminal voltage, and current.

Example

Suppose a cell has an EMF of 12 V and is connected to a circuit where the terminal voltage drops to 11.4 V when a current of 2 A flows. The internal resistance of the cell can be calculated as:

r=E−V/I
=(12−11.4)/2
r=0.3Ω

The internal resistance of the cell is 0.3 Ω.

How to Calculate Internal Resistance of a Cell

You can determine the internal resistance of a cell experimentally using a simple setup:

Experimental setup for calculating the internal resistance of a cell using a voltmeter, ammeter, and resistor.

Connect the cell to a known external resistor R.
Measure the current (I) using an ammeter.
Measure the terminal voltage (V) using a voltmeter.
Use the formula: r=E−VI_r
Repeat the experiment with different resistor values for greater accuracy.

Factors Affecting Cell Internal Resistance

Factor	Effect on Internal Resistance
Electrolyte concentration	Higher ion concentration lowers resistance.
Distance between electrodes	Greater distance increases resistance.
Temperature	Higher temperature reduces internal resistance.
Age of the cell	Old or degraded cells show higher resistance.
Electrode surface area	Larger electrode area decreases resistance.

Difference Between Resistance and Internal Resistance

Parameter	Resistance	Internal Resistance
Meaning	Opposition to current flow in an external conductor or component.	Opposition to current flow inside the cell itself.
Location	Exists in wires, resistors, and circuit elements.	Exists within the electrolyte and electrodes of the cell.
Control	Can be designed or varied as needed.	Determined by cell materials and condition.
Unit	Ohm (Ω)	Ohm (Ω)
Dependence	Depends on conductor’s material, length, and cross-section.	Depends on electrolyte properties, electrode area, and temperature.

How to Reduce Internal Resistance of a Cell

To improve a cell’s performance and reduce energy loss:

Use electrolytes with high ionic conductivity.
Maintain the cell at a stable, moderate temperature.
Ensure clean, large electrode surfaces.
Avoid deep discharge or long-term aging of the cell.

Lower internal resistance improves efficiency and helps maintain a higher terminal voltage under load.

Practical Importance

Internal resistance has a direct impact on the performance and efficiency of batteries:

Causes voltage drop during current flow.
Reduces power output and battery life.
Helps in evaluating battery health.
Plays a key role in designing EV, UPS, and power storage systems.

Conclusion

The internal resistance of a cell is a crucial factor that determines how effectively a battery can deliver current. Lower internal resistance means less energy loss, higher efficiency, and longer life. Understanding this concept helps in designing better electrical systems and maintaining battery performance.

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