Internal resistance is the opposition to the flow of current offered by the cells and batteries themselves, which leads to the generation of heat within the power source. Measured in Ohms (Ω), it represents the inherent resistance within any real-world voltage source, distinguishing it from an ideal one.
Every power source, whether a battery, a cell, or a generator, has some internal components that resist the movement of charge. This resistance causes a drop in the terminal voltage when current is drawn from the source, meaning the voltage available to the external circuit is less than the electromotive force (EMF).
Understanding the Concept
In an ideal circuit, a voltage source would supply its full electromotive force (EMF) to the external circuit. However, real-world power sources are not ideal. The materials used to construct batteries and cells—such as their electrolytes, electrodes, and connections—all contribute to this internal opposition.
When current flows through the battery, some of the electrical energy is converted into thermal energy due to this internal resistance, causing the battery to warm up. This energy loss means that the terminal voltage (the voltage measured across the battery's terminals when current is flowing) is always less than the electromotive force (the maximum potential difference the battery can provide when no current is drawn).
The Internal Resistance Formula
The relationship between a cell's electromotive force (e), the current (I) flowing through the circuit, its internal resistance (r), and the external resistance (R) is described by the formula:
e = I (r + R)
This equation is a direct application of Ohm's Law, extended to account for the internal voltage drop within the power source.
Let's break down the components of this formula:
| Component | Symbol | Description |
|---|---|---|
| Electromotive Force | e (or EMF) | The total potential difference generated by the cell or battery when no current is flowing (i.e., open circuit voltage). Measured in Volts (V). |
| Current | I | The total current flowing through the circuit, both internally and externally. Measured in Amperes (A). |
| Internal Resistance | r | The inherent resistance within the power source itself. Measured in Ohms (Ω). |
| External Resistance | R | The resistance of the external circuit connected to the power source (e.g., a light bulb, a motor). Measured in Ohms (Ω). |
Practical Implications
Internal resistance is a critical factor in the performance and efficiency of power sources:
- Voltage Drop: As current increases, the voltage drop across the internal resistance (Ir) also increases, leading to a lower terminal voltage for the external circuit.
- Heat Generation: The energy dissipated as heat (I²r) reduces the efficiency of the power source and can lead to overheating, potentially damaging the battery or shortening its lifespan.
- Power Output: There's an optimal external resistance for which the power delivered to the external circuit is maximized. This occurs when the external resistance equals the internal resistance (R = r).
- Battery Life: Higher internal resistance indicates an older or degraded battery, as the materials within the battery change over time, increasing their opposition to current flow. This is why old batteries "die" even if they show a good open-circuit voltage; they can't supply enough current without a significant voltage drop.
Understanding internal resistance is crucial for designing efficient circuits and for evaluating the health and performance of batteries and power supplies. For a deeper understanding of voltage and current relationships, you can explore the principles of Ohm's Law.
