Norton's theorem states that any two terminal
voltage source can be represented by a constant
current source
with internal parallel resistance R_{int} as in the circuit below:

The values for I_{SC} and R_{int} can either be calculated or measured.

When calculating,
first use
Kirchhoff's or
superposition to compute the open circuit voltage V_{OC}.
Next calculate the value of R_{int} by replacing all voltage sources by their internal resistances.
The value of I_{SC}is V_{OC}/R_{int}.

To measure, first find the short circuit
current from A to B and call this I_{SC}.
Next measure the open circuit voltage (V_{OC}).
The value of R_{int} is V_{OC}/I_{SC}.

We'll calculate and measure the values for I_{SC}, V_{OC} and R_{int} for the circuit below.

We can use Kirchhoff's voltage law to give us the current:

5 - 2.8 = I*(100+33+33) 2.2 = I*166. I = 2.2/166 = 0.013

Now V_{OC} is V_{CD}, so:

V_{OC} = 2.8 + 0.013*33 = 3.23

For R_{int} we short all voltage sources (assuming no internal resistance) and this
gives the following circuit:

The
calculation of R_{int} is quite easy:

R_{int} = 100 + 1/(1/33 + 1/133) = 100 + 26.4 = 126.4

From this we can calculate the short circuit current:

I_{SC} = 3.23 / 126.4 = 0.0255.

The circuit was built and using a multimeter the value of V_{OC}(V_{CD}) was 3.3V.
The short circuit current I_{SC} was measured to be 25.6mA.
From this we can calculate R_{int}:

R_{int} = 3.3/0.0256 = 128.9

The table below shows how close the actual measurements were to the theoretical calculations.

V_{OC} | I_{SC} | R_{int} | |
---|---|---|---|

Measured | 3.3 | 0.0256 | 128.9 |

Calculated | 3.23 | 0.0255 | 126.4 |

Fischer-Cripps. A.C., *The Electronics Companion.* Institute of Physics, 2005.

Copyright © 2014 Barry Watson. All rights reserved.