# Physics A level revision resource: Investigating electromotive force

Electromotive force (EMF) is equal to the terminal potential difference when no current flows. EMF and terminal potential difference (V) are both measured in volts; however, they are not the same thing. EMF (ϵ) is the amount of energy (E) provided by the battery to each coulomb of charge (Q) passing through.

## How do we calculate EMF?

The EMF can be written in terms of the internal resistance of the battery (r) where: ϵ = I(r+R)

Which from Ohm’s law, we can then rearrange this in terms of the terminal resistance: ϵ = V+Ir

The EMF of the cell can be determined by measuring the voltage across the cell using a voltmeter and the current in the circuit using an ammeter for various resistances. We can then set up a circuit to determine EMF as shown.

## How does Faraday's law relate to EMF?

Faraday’s law states that any change in the magnetic field of a coil will act to induce an EMF in the coil (and hence also a current). It is proportional to minus the rate of change in magnetic flux (ϕ) (note N is the number of turns in the coil).

Using Faraday’s law, society has benefited from important technology such as transformers which are used in the transmission of electricity in the UK national grid which is now a necessity of our homes. Also it is used in the electric generators and motors such as hydroelectric dams, which produce the electricity that is now integral to our modern technological needs. A current research project at Birmingham, MAG-DRIVE, is finding ways to develop and improve permanent magnet materials that can be used in the next generation of electric vehicles. EMF is also generated from solar cells so it is important in renewable energy research topics.

## Laboratory Confessions

In the Laboratory Confessions podcast researchers talk about their laboratory experiences in the context of A Level practical assessments. Episodes that cover the appropriate use of digital instruments (simple harmonic motion), correct construction of circuit diagrams (resistivity in a wire) and the use of DC power supplies (capacitors) are all relevant to the EMF experiment, below you can hear the resistivity in a wire podcast.

## How do we interpret our data?

As the resistance increases in the variable resistor, the amount of current will decrease. Plotting the voltage against current should produce a linear relationship, where the gradient of the line gives the negative internal resistance of the cell (-r) and the intercept gives the EMF (the voltage at which the current is 0).

Taking multiple readings at different resistance values will give more points on the V-I plot, making the fit more reliable. it is also a good idea do repeat measurements as the cell will gradually drain, which will affect the readings. To prevent the cell/battery from draining out, it should be disconnected between readings. Alternatively, a switch could be included in the circuit. Also be it is advisable not to use a rechargeable battery as these tend to have low internal resistances.

Whilst this experiment is quite simple, it will help you distinguish between the terminal difference and the EMF, which can be a difficult concept for students to understand. Since humans are becoming ever more reliant on electricity, the research that involve EMF is important for the development and technological advances of electricity.