4.2.2 - E.m.f., p.d. and energy transfer

Potential difference and the volt

Potential difference, usually shortened to p.d., tells you how much energy is transferred for each coulomb of charge passing between two points or through a component.

If a lamp has a p.d. of $3.0\,\mathrm{V}$ across it, each coulomb of charge passing through the lamp transfers $3.0\,\mathrm{J}$ of energy to the lamp and its surroundings. The charge is not "used up"; the energy carried by each coulomb is reduced.

The unit statement is not separate from the definition. Since p.d. is energy per unit charge,

Here $V$ is potential difference in volts, $W$ is energy transferred or work done in joules, and $Q$ is charge in coulombs.

Worked example: energy transferred in a lamp

A charge of $4.0\ \text{C}$ passes through a lamp with a p.d. of $3.0\ \text{V}$ across it. Calculate the energy transferred to the lamp.

Use:

Substitute:

So $12\ \text{J}$ of energy is transferred from electrical energy to the lamp.

More generally, the p.d. between two points is the work transferred per unit charge between those points. For a resistor, electrical energy is transferred to thermal energy. Across a source, charge gains electrical energy. The sign of a measured p.d. depends on which point is used as the reference; it does not make the amount of energy transferred negative.

E.m.f. as source energy per charge

Electromotive force, e.m.f., is also measured in volts, but it describes a source rather than a component using energy.

Despite its name, e.m.f. is not a force and is not measured in newtons. A cell with e.m.f. $1.5\ \text{V}$ transfers $1.5\ \text{J}$ of chemical energy into electrical energy for each coulomb of charge passing through the cell.

OCR commonly denotes e.m.f. by $E$, and some textbooks use $\mathcal{E}$. In this lesson, $\mathcal{E}$ means e.m.f. so that it is not confused with $W$, the energy transferred.

The key distinction is the direction of energy transfer:

In an ideal circuit with one external component and negligible losses, the p.d. across the component can have the same numerical value as the source e.m.f. That does not make the meanings identical: the source supplies energy per coulomb, while the component transfers energy per coulomb out of the electrical store.

[DIAGRAM: asset_slug: 4_02_2_emf_pd_and_energy_transfer__diagram_01; description: A source supplies energy per coulomb and a lamp transfers that energy while charge is conserved.; caption: A source supplies energy per coulomb and a lamp transfers that energy.]

Energy transfer calculations

The formula $V = W/Q$ rearranges to the most useful calculation form:

For a source, the same energy-per-charge idea gives:

In OCR notation this may be written as $W = EQ$, where $E$ means e.m.f. Be careful: $W$ is the energy transferred, not $E$.

Worked example: energy supplied by a power supply

A power supply has e.m.f. $6.0\ \text{V}$. A total charge of $12\ \text{C}$ passes through the supply. Calculate the energy transferred into electrical energy.

The supply transfers $72\ \text{J}$ into electrical energy.

Worked example: using current to find charge first

A component has a p.d. of $4.5\ \text{V}$ across it. A steady current of $0.80\ \text{A}$ flows for $25\ \text{s}$. Calculate the energy transferred in the component.

First find the charge using $Q = It$:

Then use $W = VQ$:

This link uses the earlier current definition, $I = Q/t$. The main energy relationship in this lesson remains $W = VQ$; power relationships are treated separately later.