D.C. Theory © copyright M.J.Morris 2004 |

In the electrical circuits we have looked at so far we have regarded the voltage source supplying the circuit as being a perfect voltage source.

- We have assumed that the voltage supplied to the circuit remains constant regardless of how much current is being supplied.
- We have also assumed that the power supply provides energy and that all of this energy is converted to heat by the resistance in the external circuit.

In practice this is not the case.

- The terminal voltage of a battery decreases as the current it supplies to a circuit increases. This is the same for all real voltage sources. (However power supply designers do produce stabilised power supplies where feedback circuits are used to maintain a relatively constant output voltage).
- All power supplies get warm during use which illustrates that some of the energy that they provide is actually being converted to heat inside the power supply itself.

At first sight this variation of supply voltage appears to be a difficult problem to deal with because the actual reasons for the variation are different for each of the several different voltage sources we use. e.g.

- For a battery: the voltage drops because the rate of chemical reactions transferring charge to the battery terminals cannot match the rate at which the charge is leaving the terminals to flow around the circuit
- For a generator: the current produces stronger magnetic fields inside the generator which slow the generator and reduce the supply voltage.

Fortunately regardless of the actual nature of the power supply we can model its behaviour with two simple electrical components, an e.m.f. in series with an internal resistance. This is called a power supply model. With this model then the circuit current also flows through an internal resistance. This produces an internal voltage drop inside the power supply. This internal voltage drop therefore reduces the voltage across the power supply terminals. The power dissipated by the internal resistance represents the heat generated by the power supply.

The terminal voltage (V) is equal to the e.m.f. voltage (E) minus the internal voltage drop (Ir)

(using ohms law :- internal voltage drop = current (I) x internal resistance (r))

- V = E - Ir

To model any real power supply we just have to determine the correct values of E and r to use.

When the power supply is not connected to a circuit there will be no current flowing therefore:

- V = E - 0 x r
- V = E
- ie the e.m.f voltage is equal to the open circuit terminal voltage of the power supply.

The internal resistance can be determined by connecting a circuit of known resistance and measuring the current that flows

- I = E/(R + r)
- therefore r = (E/I) - R

The power supplied by the e.m.f. is given by P = EI and the power dissipated in the power supply is given by P = I^{2}r

The energy provided by the e.m.f. is given by W = EIt and the energy dissipated in the power supply is given by W =I^{2}rt