E.m.f. and p.d (4.2.2)
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Potential difference is defined as the energy transferred per unit charge.
When a circuit component has a potential difference across it, electrical energy is transferred from the power supply to the charge carriers and then to the component. The greater the difference in electric potential between the battery terminals, the more energy each coulomb of charge receives as it passes through the cell.
An example of energy transfer is a filament bulb connected to a battery. The bulb converts electrical energy into light and thermal energy. A battery with a higher potential difference between its positive and negative terminals supplies more energy per unit charge, so it charges the bulb with more energy each second, making it shine more brightly.
The potential difference across a component is given by the equation:
Where:
- is the energy in joules transferred to the component ,
- is the charge in coulombs passing through the component, and
- Potential difference is measured in volts
It is important to note that is the potential difference across a component when of energy is transferred to the component by of charge, meaning that:
The potential difference across a component in a circuit is measured by connecting a voltmeter in parallel to the component. The circuit symbol for a voltmeter is a circle with a capital V in the centre.
For example, the diagram below shows a voltmeter connected in parallel to a filament bulb.
A voltmeter can be assumed to have infinite resistance, so that no current flows through it when it is connected in parallel to a component.
Note that in reality, a very small, non-zero current must flow through the voltmeter. This current is required for the voltmeter to function and measure the energy carried by each charge.
The electromotive force (EMF) of a power source is the amount of energy converted to electrical energy per unit charge.
EMF is similar to potential difference but is used when work is done on the charge carriers, such as by a power source like a cell or battery.
Examples of this include:
- Common batteries used in electrical circuits convert chemical energy into electrical energy.
- Solar cells, which convert light energy into electrical energy, and thermocouples which convert thermal energy into electrical energy.
EMF in is given by the formula:
Where:
- is the work done in on the charges by the power source
- is the charge in passing through the power source.
It is important to note that EMF is not a force and is measured in volts the same as potential difference.
Moreover, the word ‘force’ in electromotive force originates from the way a power source transfers energy to the charges moving through it, which drives them around a circuit.
EMF and potential difference are both measured in and are both defined as the energy transferred per unit charge. However, they both have a discrete key distinction:
- EMF is used when work is done on the charge carriers, and the charge carriers gain energy.
- Potential difference is used when work is done by the charge carriers, and the charge carriers lose energy.
An example of this is illustrated in the diagram above.
- Work is done on charge carriers as they move through a battery and are given energy.
- However, work is done by the charge carriers when they move through a filament bulb; the electrical energy of the charge carriers is converted into thermal energy and light energy.
The energy transferred to electric charges passing through a component due to an electromotive force (EMF) or a potential difference (p.d.) can be found using similar equations.
The energy transferred to a charge passing through a component with EMF, is:
The energy transferred by a charge passing through a component with p.d. is given by the formula:
- A greater EMF or p.d. leads to a greater energy transfer.
- A greater charge also leads to a greater energy transfer.
- The energy transfer to or from the charges is equal to the work done on or by the charges.
Charged particles are accelerated by an electric field.
An electric field can be formed by applying a potential difference between an anode – a positively charged electrode – and a cathode; a negatively charged electrode.
An example of this is illustrated in the diagram below. An electric field (represented by green arrows) forms between a cathode and an anode.
When drawing an electric field, the arrows represent the direction that positive charges, such as protons, would flow. They are repelled away from the positive anode and attracted towards the negative cathode.
Negatively charged particles, such as electrons, are accelerated in the opposite direction. They are repelled away from the negative cathode and attracted towards the positive anode.
When charged particles are accelerated by an electric field, the kinetic energy gained by a particle accelerated from rest by a potential difference, is given by:
Where:
- is the mass of the particle in
- is the final speed of the particle in
- is the charge of the particle in
Electrons are accelerated by a potential difference in an electron gun.
- In an electron gun, a heated filament is placed inside a vacuum tube opposite a positive anode.
- Electrons are emitted from the heated filament by thermionic emission.
- A potential difference is applied to the heated filament, causing it to act as a negative cathode.
- Electrons accelerate from the negative cathode to the positive anode and pass through a small hole in the anode.
Electrons have a charge equal to the elementary charge so the electrons have a kinetic energy of:
on leaving the electron gun. Electron beams produce a narrow beam of electrons that can be used to ionise particles.