Question

What is Electromotive Force (EMF)? How is it different from potential difference?

Answer 1

The Water Pump Analogy

Imagine a water circuit with a pump and a water wheel.

• The Pump: The pump does work on the water, lifting it up and giving it potential energy. It's the source of the energy that makes the water flow.
• The Water Wheel: As the water flows down from its high point, it turns a water wheel, doing work. The water loses its potential energy as it passes through the wheel.
• The Height Difference:
  • The total height the pump is capable of lifting the water is the Electromotive Force (EMF).
  • The actual height difference across the water wheel (where the energy is used) is the Potential Difference (PD).

Now, imagine the pump itself isn't perfect; it has some internal friction. To pump the water, it has to use a little bit of its own energy just to overcome this internal friction. Therefore, the height the water reaches outside the pump is slightly less than the pump's maximum theoretical lifting height. This is the key to the difference.

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What is Electromotive Force (EMF)?

Electromotive Force (EMF, symbolized by $\mathcal{E}$) is the total energy supplied by a source (like a battery or generator) per unit of electric charge.

• Misleading Name: The term "force" is historical and misleading. EMF is not a force. It's a measure of energy per charge, so its unit is the Volt (V), which is a Joule per Coulomb.
• The Cause: EMF is the cause of the electric current. It's the "push" that a source provides to the charges.
• Energy Conversion: It represents the work done by a non-electrical process to move charge. For example:
  • In a battery: Chemical reactions convert chemical energy into electrical potential energy.
  • In a generator: A changing magnetic field converts mechanical energy into electrical potential energy.
  • In a solar cell: Light energy is converted into electrical potential energy.

In short: EMF is the ideal, maximum voltage a source can provide when no current is being drawn from it (an open circuit).

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What is Potential Difference (PD)?

Potential Difference (PD, symbolized by $V$ or $\Delta V$), often just called voltage, is the energy lost or work done by a unit of charge as it moves between two points in a circuit.

• The Effect: If EMF is the cause, Potential Difference is the effect of current flowing through a component.
• Energy Dissipation: It represents the energy converted from electrical potential energy into other forms (like heat in a resistor, light in an LED, or sound in a speaker).
• Measurement: It is measured across a component in a circuit (e.g., across a resistor or a light bulb).

In short: Potential Difference is the actual energy per charge that is used by a component or available across the terminals of a source when current is flowing.

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The Key Difference: Internal Resistance

The main reason EMF and Potential Difference are not always the same for a source is internal resistance ($r$).

Every real-world energy source (like a battery) has some internal resistance. It's like the internal friction in our water pump analogy.

• When a battery is not connected to anything (an open circuit), no current flows ($I=0$). The voltage you measure across its terminals is its full EMF.
• When the battery is connected to a circuit (a closed circuit), current ($I$) starts to flow. This current must also flow through the battery's own internal resistance. As it does, some voltage is "lost" or "dropped" inside the battery itself. This internal voltage drop is equal to $I \times r$.

This leads to the crucial relationship:

$V = \mathcal{E} - Ir$

Where:
$V$ is the Terminal Potential Difference (the actual voltage available to the external circuit).
$\mathcal{E}$ is the Electromotive Force (the ideal, total voltage of the source).
$I$ is the current flowing.
$r$ is the internal resistance of the source.

Because of the $Ir$ term, the terminal potential difference ($V$) will always be less than the EMF ($\mathcal{E}$) when the source is supplying current.

Comparison Table

| Feature | Electromotive Force (EMF) | Potential Difference (PD) |
| :--- | :--- | :--- |
| Definition | Total energy supplied per unit charge by a source. | Energy dissipated per unit charge between two points in a circuit. |
| Nature | It is the cause of the current. | It is the effect of the current flowing through a component. |
| Source/Component| Associated with an energy source (battery, generator). | Associated with any component in a circuit (resistor, lamp, and also the terminals of a source). |
| Magnitude | For a source, EMF is always greater than the potential difference across its terminals when supplying current. | For a source, PD is less than its EMF (when supplying current). |
| Measurement | Measured in an open circuit (no current flowing). You measure the voltage across a battery's terminals when it's not connected to anything. | Measured in a closed circuit (current is flowing). You measure the voltage across a component while it is operating. |
| Dependency | Independent of the circuit's resistance. It's a property of the source itself. | Depends on the resistance of the component it is measured across ($V=IR$). |
| Symbol | $\mathcal{E}$ (or sometimes E) | $V$ or $\Delta V$ |
| Formula Context | $\mathcal{E} = I(R + r)$ (Total voltage for the whole circuit) | $V = IR$ (Voltage across an external component) or $V = \mathcal{E} - Ir$ (Terminal voltage of the source) |

Summary

• EMF ($\mathcal{E}$) is the battery's full, ideal potential—the "listed voltage." It's the energy provider.
• Potential Difference ($V$) is the actual voltage available to the external circuit after the battery has "paid a tax" to its own internal resistance. It's the energy user.

You can only get the full EMF from a battery if you draw no current from it. The moment you use it, the terminal voltage drops slightly.