6.07 Internal resistance

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.

In practice this is not the case.

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.

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.

internal resistance

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))

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:

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

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 = I2r
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 =I2rt