Internal Resistance: The Hidden Battle Inside Every Battery
What Exactly is Internal Resistance?
Imagine a perfect, ideal battery. When you connect it to a circuit, it would always provide exactly the same voltage, no matter how much current you draw from it. In the real world, such a perfect power source does not exist. Every real battery, generator, or solar cell has a built-in opposition to the flow of electric current within itself. This opposition is called internal resistance, symbolized by $r$.
Think of it like a water pump. A perfect pump would send water out with immense force. But if the pump's internal pipes were narrow and clogged, the water coming out would have less force, especially when you try to get a lot of water out quickly. Similarly, the internal resistance acts like a tiny, invisible resistor inside the power source, "using up" some of the energy and reducing the voltage available to the outside circuit.
The Real Battery: A Simple Model
To understand how internal resistance affects a circuit, we use a very useful model. We represent a real battery as a combination of two perfect, imaginary components:
- An ideal voltage source ($E$ or $V_{emf}$): This provides a constant, unchanging voltage. It is also known as the Electromotive Force[1] or EMF. This is the voltage you would measure when the battery is not connected to anything.
- A small internal resistor ($r$): This represents the internal resistance, connected in series with the ideal voltage source.
When you connect this "real battery" model to an external resistor ($R$), the internal resistor ($r$) and the external resistor ($R$) form a simple series circuit.
The Key Formula: Terminal Voltage
The voltage you actually measure across the battery's terminals when it's connected to a circuit is called the terminal voltage ($V_{terminal}$). It is always less than the EMF due to the voltage "lost" across the internal resistance.
$V_{terminal} = EMF - (I \times r)$
Where:
- $V_{terminal}$ is the voltage measured when the battery is in use (Volts, V).
- $EMF$ is the ideal, no-load voltage of the battery (Volts, V).
- $I$ is the current flowing through the circuit (Amperes, A).
- $r$ is the internal resistance (Ohms, $\Omega$).
The term $I \times r$ is the "lost volts."
Where Does Internal Resistance Come From?
Internal resistance isn't a single thing; it's the sum of several small resistances within the power source. The main contributors are:
- Resistance of the Materials: The electrodes (terminals) and the internal connectors inside the battery are made of materials like metals, which have a small but measurable resistance.
- Resistance of the Electrolyte: The chemical paste or liquid inside a battery that allows ions to flow (the electrolyte) is not a perfect conductor. Ions move through it with some difficulty, creating resistance.
- Chemical Reaction Limits: The speed at which the chemical reactions can occur at the electrodes also acts as a form of resistance. If the reactions can't keep up with the demand for current, the voltage drops.
These factors mean that internal resistance is not a fixed, constant value. It changes with:
- Age: As a battery gets older, its internal resistance increases. The chemicals get used up, and the electrodes can corrode.
- Temperature: For most batteries, internal resistance decreases as temperature increases (just like most conductors). A cold car battery has a much harder time starting an engine.
- State of Charge: A fully charged battery has a lower internal resistance than a nearly empty one.
| Factor | Effect on Internal Resistance | Real-World Example |
|---|---|---|
| Age of Battery | Increases significantly | An old phone battery dies quickly even at 30% charge. |
| Temperature | Decreases when warm, increases when cold | A car struggles to start on a freezing morning. |
| State of Charge | Increases as the battery discharges | A flashlight dims as its batteries run down. |
| Battery Size & Type | Larger batteries typically have lower $r$ | A car battery can deliver hundreds of Amps, a AA battery cannot. |
Putting It All Together: A Practical Example
Let's see internal resistance in action with a common scenario: starting a car.
You have a $12\text{V}$ car battery with an internal resistance of $0.01\ \Omega$. When you turn on the headlights (a small load, drawing about $5\text{A}$), the lost volts are: $I \times r = 5 \times 0.01 = 0.05\text{V}$. The terminal voltage is $12 - 0.05 = 11.95\text{V}$. You barely notice the drop.
Now, you turn the key to start the engine. The starter motor is a huge load, drawing $200\text{A}$. Now the lost volts are: $I \times r = 200 \times 0.01 = 2\text{V}$. The terminal voltage plummets to $12 - 2 = 10\text{V}$. This is why the headlights often dim momentarily when you start the car—the available voltage for the entire electrical system has dropped significantly because of the large current and the internal resistance.
Using the real battery model, the total resistance in the circuit is the external resistance plus the internal resistance ($R + r$). The current flowing is given by Ohm's Law:
$I = \frac{EMF}{R + r}$
This shows that the internal resistance directly limits the maximum current a battery can supply.
Consequences and The Danger of Short Circuits
The most dramatic demonstration of internal resistance is a short circuit. A short circuit occurs when the two terminals of a battery are connected with a very low resistance path, like a piece of thick metal wire. In this case, the external resistance $R \approx 0$.
Let's see what happens with our car battery example. If we short-circuit it, the current would be:
$I = \frac{12\text{V}}{0\ \Omega + 0.01\ \Omega} = \frac{12}{0.01} = 1200\text{A}$
That's an enormous current! However, the terminal voltage under this condition would be:
$V_{terminal} = 12\text{V} - (1200\text{A} \times 0.01\ \Omega) = 12\text{V} - 12\text{V} = 0\text{V}$
All the energy from the EMF is being "used up" inside the battery itself, across its internal resistance. The power dissipated inside the battery is $P = I^2 \times r = (1200)^2 \times 0.01 = 14,400\text{W}$! This is a massive amount of heat, which will cause the battery to get very hot, very quickly, potentially causing it to leak, melt, or even explode. This is why short-circuiting batteries is extremely dangerous. The internal resistance is the only thing limiting the current in a short-circuit scenario, and it's often not enough to prevent damage.
Common Mistakes and Important Questions
Q: Is internal resistance a good thing or a bad thing?
Q: Why does my phone get warm when I'm using it and charging it at the same time?
Q: How can I measure the internal resistance of a battery?
A: A simple method involves two measurements:
- Measure the voltage across the battery terminals when it's not connected to anything. This is the EMF.
- Connect a known resistor ($R$) across the terminals and measure the terminal voltage ($V_t$) and the current ($I$).
You can then use the formula $r = \frac{EMF - V_t}{I}$ to calculate the internal resistance.
Internal resistance is the unavoidable, inherent resistance within every real-world power source. It explains why batteries and generators are not 100% efficient and why their output voltage drops under load. By modeling a power source as an ideal voltage source in series with a small resistor, we can accurately predict circuit behavior, understand real-world phenomena like dimming headlights and battery warming, and appreciate the critical safety role internal resistance plays in limiting short-circuit currents. Grasping this concept is a fundamental step in moving from ideal, textbook electronics to understanding and working with the practical, imperfect components we use every day.
Footnote
[1] EMF (Electromotive Force): Despite its name, it is not a force. It is the maximum potential difference, or voltage, generated by a source such as a battery or generator when no current is flowing. It is measured in Volts (V).