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. i.e.:

Electrical potential

In practice this is not the case as:

  1. 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).
  2. All power supplies get warm during use which shows that some of the energy that they provide is actually being converted to heat inside the power supply itself!

This is illustrated in the animation below

internal resistance

This variation of supply voltage is potentially a difficult thing to explain, especially as the actual reasons for the variation would depend on the type of power supply being used.
For example:-

Fortunately we can avoid these details and regardless of the actual nature of the power supply we can represent it with a power supply model which consists of only simple electrical components. One way of doing this is by representing the power supply as a perfect voltage source (an e.m.f.) in series with an internal resistance. With this power supply model is applied to an external circuit then the circuit current also flows through the internal resistance. This produces an internal voltage drop inside the power supply which therefore reduces the voltage across the power supply terminals. The power dissipated by the internal resistance represents the heat generated in the power supply. This is illustrated in the animation below.

internal resistance

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