EMF and Potential Difference

So far we have talked about current and charge, but not about what makes the current flow in the first place. That "push" is provided by a source of EMF — typically a battery, cell, generator, solar panel or dynamo — and the energy transfer associated with moving charges is measured by the potential difference across components.

At first glance EMF (electromotive force) and potential difference (pd) appear to be the same thing. They have the same units and are often numerically close. But they refer to different physical processes, and OCR examiners routinely ask students to distinguish them. This lesson nails the definitions, the differences and the applications.

This is OCR A-Level Physics A Module 4.2.2 (Energy, power and resistance) and Module 4.3.1 (DC circuits).

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Defining Potential Difference

Potential difference (symbol V, sometimes pd) across a component is the energy transferred from the electrical energy of the charges into some other form per unit charge passing through.

Formally:

V = W / Q

where W is the energy transferred (in joules) as charge Q (in coulombs) passes through the component.

The unit is the volt (V), defined as 1 V = 1 J C⁻¹.

So "the pd across this bulb is 6 V" means: for every coulomb of charge that passes through the bulb, 6 joules of electrical energy are converted into light and heat.

Worked Example

A current of 0.30 A flows through a 12 V lamp for 15 s. Calculate the energy transferred.

• Q = It = 0.30 × 15 = 4.5 C
• W = VQ = 12 × 4.5 = 54 J

(Or directly: W = VIt = 12 × 0.30 × 15 = 54 J.)

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Defining EMF

EMF (electromotive force, symbol ε, the Greek letter epsilon) is the energy transferred from some other form into the electrical energy of the charges per unit charge, within the source.

Formally:

ε = W / Q

Notice that the equation has exactly the same mathematical form as the pd equation, and the same unit (the volt). But the physical process is the opposite: chemical energy (in a battery) or mechanical energy (in a dynamo) is converted into electrical energy as charge passes through the source.

Despite its name, EMF is not a force. It is an energy transfer per unit charge — a sort of electrical "pressure" — measured in volts. The old 19th-century name "electromotive force" is misleading but has stuck.

Worked Example

A battery drives 3.0 C of charge around a circuit and in doing so transfers 18 J of chemical energy into electrical energy. What is its EMF?

• ε = W / Q = 18 / 3.0 = 6.0 V

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The Key Difference — EMF vs PD

Here is the distinction OCR loves to test:

Quantity	Where the energy transfer happens	Direction of transfer
EMF (ε)	Inside a source of electrical energy (battery, cell, generator)	Other form → electrical
Potential difference (V)	Across a component that consumes electrical energy (resistor, bulb, motor)	Electrical → other form

Exam Tip: A gold-standard OCR-style answer: "EMF is the energy transferred from chemical (or other) energy to electrical energy per unit charge by the source. Potential difference is the energy transferred from electrical energy to other forms per unit charge by a component."

This distinction becomes critical in Lesson 9 on internal resistance, where we will see that the terminal pd of a battery can be less than its EMF when the battery is delivering current, because some of the electrical energy is dissipated inside the battery itself.

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The Volt — A Deeper Look

From V = W/Q we get 1 V = 1 J / 1 C = 1 J C⁻¹. So a volt is really "joules per coulomb" — an energy per unit charge. This is a far more physical way to think about voltage than "how much push".

Some useful consequences:

• The energy gained by a charge Q moving through a pd V (e.g. an electron crossing a capacitor) is W = QV.
• The energy lost by a charge Q passing through a resistor with pd V is W = QV.
• The power dissipated by the resistor is then P = W/t = VI (since Q/t = I).

We will develop the power equations fully in Lesson 8.