## EMF

Glossary Definition for 16-19

#### Description

EMF is an abbreviation for electromotive force. It is a measure of the ability to drive an electric current. The EMF of any electrical power supply, such as a cell, a battery or a dynamo, is defined as the work that the supply would do, per unit charge, to move charge around a circuit if the supply were connected into the circuit,

ℰ = WQ

where ℰ is the EMF of the supply, and W is the work done in moving charge Q around the circuit.

#### Discussion

For historical reasons its name includes the word ‘force’, but it is important to recognise that an EMF is not a force.

An EMF may be generated, for example, by chemical reactions, as in a cell or battery, or by changes in the magnetic flux through a circuit, as in a dynamo or generator.

The potential difference, V, across the terminals of a real power supply that is driving a current around a circuit, is less than its EMF. This is because some of the energy supplied by the power supply is dissipated inside the power supply itself. This is often modelled by assigning an internal resistance r to the power supply, defined by

V = ℰ − Ir

where the quantity Ir is the difference between the EMF of a power supply and the potential difference across its terminals, and is sometimes referred to as the ‘lost volts’. See Figure 1. Figure 1: A conceptual representation of a real power supply, modelled as an ideal power supply of EMF ℰ, and an internal resistance r.

volt, V

A-1 kg m2 s-3

none

#### Mathematical expressions

• ℰ = WQ

• where ℰ is the EMF of the supply, and W is the work to move charge Q round the circuit.
• For a generator,
• ℰ = -d(NΦ)dt

is the EMF induced in a coil with N turns. Here, N is the number of turns in the generator coil and Φ is the magnetic flux through each turn of the coil.
• When a power supply drives a current, the terminal potential difference is less than the EMF according to the equation
• V = ℰ − Ir

where V is the terminal potential difference, I the current through the power supply and r the internal resistance of the power supply.

#### Related entries

• Electrical potential difference
• Electric charge
• Magnetic flux

#### In context

A typical fresh alkaline manganese cell with a terminal potential difference of 1.5 V, and an internal resistance of 0.21 Ω, driving a current of 250 mA has an EMF of approximately

1.55 V + (0.25 A  ×  0.21 Ω) = 1.55 V

Each of the six generators at Drax Power Station in Yorkshire produces an EMF of 23,500 V.

#### References

http://data.energizer.com/pdfs/alkaline_appman.pdf

https://www.power-technology.com/projects/drax/