EMF and Energy per Unit Charge

A source such as a cell lifts electric charge to higher electric potential by changing chemical or mechanical energy into electrical energy.

A 1.5 V cell supplies 1.5 joules of electrical energy to each coulomb of charge that passes through the cell.

EMF and potential difference use the same unit, but they describe different parts of the energy journey: the source supplies energy, while circuit components receive or convert it.

Electromotive force is the work done by a source on each unit of charge as the source converts non-electrical energy into electrical potential energy. It is represented by ε.

What a source does

Inside a cell, chemical forces move charge from lower electric potential to higher electric potential, against the electrostatic tendency. A generator performs the same energy-raising role using mechanical input.

The source is therefore an energy converter and a charge pump. It does not create charge; charge already exists throughout the complete circuit.

Definition and mathematical form

If ε is constant, doubling the charge doubles the total energy supplied. The emf itself remains energy per coulomb, not total energy.

Why emf is measured in volts

Because emf is WQ, its unit is J/C, which is the volt. The historical name electromotive force can be misleading: emf is not measured in newtons and is not a mechanical force.

EMF compared with potential difference

Both quantities are energy per coulomb. Their distinction comes from the role of the device: a source raises the electrical energy of charge, whereas a load usually lowers it by transferring energy to heat, light or motion.

Connection with terminal potential difference

In a real discharging cell, some energy per coulomb is transferred in the internal resistance. The energy balance is:

When the circuit is open, I=0 and the internal drop vanishes, so a high-resistance voltmeter measures V≈ε.

Power supplied by a source

If the source supplies ε joules to every coulomb and I coulombs pass each second, its rate of supplying energy is:

For a discharging real source, this power separates into external output and internal heating.

This power equation is the same energy accounting as ε=V+Ir, multiplied by current.

Cells in series

If identical cells are connected in series with the same orientation, each supplies energy per coulomb in turn. Their emfs add.

Reversing a cell reverses its contribution, so signs must follow the chosen circuit direction.

Worked example 1: energy

A 9.0 V battery transfers 20 C through itself.

Worked example 2: charge and electrons

A 6.0 V source supplies 300 J. Find the charge transferred.

How to interpret source labels

A 12 V battery label means 12 J of energy are supplied per coulomb under the stated source conditions. It does not mean the battery contains only 12 J, nor does it state the current without information about the connected circuit.

Exam-ready reasoning

• Define emf as energy supplied per unit charge.
• State clearly that emf is not a force.
• Use ε=WQ and 1 V=1 J/C.
• Contrast the source's energy gain with a load's energy transfer.
• Connect emf to terminal voltage using V=ε−Ir during discharge.
• Use P=εI when the rate of source energy conversion is required.