e.m.f.

e.m.f. stands for electromotive force, given the symbol E and has the SI units of Volts, V.

e.m.f. however, is not a force but an increase in potential (energy). Cells, batteries, dynamos, solar pannels etc produce a potential difference that can induce current. This potential differnce requires a different name from the voltage across a resistor. A resistor causes a decrease in potential as energy leaves the circuit normally in the form of heat.

Definition

The e.m.f. of a source (a device which supplies electrical energy) is defined as the energy converted to electrical energy when unit of charge (i.e. 1 coulomb) passes through it.

Terminal potential difference

Definition

The terminal p.d. of a source is the potential difference across its terminals, it is often given the symbol V.

Internal resistance

While a cell gives electrons energy to flow and form a current, some of that energy is used up by movement in the cell itself. This is why batterries become warm after extented use. The cell itself has a resistance which the electrons have to overcome, this is called the internal resistance and is given the symbol r or Rinternal, and has the SI units of ohms.

The result of this is that as more current is drawn the terminal p.d. will drop. We model this by thinking of a cell as a source of e.m.f. in series with a resistor whose resistance is the internal resistance.

FIG 1: Internal Resistance Model

When there is no current flowing then the terminal p.d. is the same as the e.m.f. as there is no potential drop over the internal resistance (using Vinternal=IRinternal when I=0).

When current flows however energy (potential) is lost overcoming internal resistance and the terminal voltage decreases. The e.m.f., internal resistance and current drawn can be linked by the following equation:

V = E - IRinternal

Load

The load on a power supply is the rest of the circuit attached to it. When considering ohm's law we should rewrite it as follows:

V = IRload
where I = is the current drawn from the source and Rload is the external load resistance in the circuit.

Conclusion

When undertaking the detailed design of circuits (e.g. sensor systems) we need to consider the internal resistance and lost volts. This can be done using the model in Fig 1 and kirchoff's laws. In practice we try to draw as little current as possible by having high load resistances, this minimises the lost volts and so the source provides more consistant output.