Circuit Design Considerations?

Question

If you were given an equivalent resistance and you were asked to design a circuit containing only resistors that must have an equivalent resistance equal to that of the given, how would you do it?

I mean, is there a systematic way of doing it, or you just have to try and try combinations until you get the resistance?

Answer 1

How you would do it would depend on how many resistors you had to use and the topology of the required circuit.

Answer 2

The quick solution is to design a circuit with one resistor, matching the target resistance.

Another quick solution is to give a circuit with 2 resistors in series that are 1/2 the target resistance each (since resistors in parallel add).  e.g. If your target resistance is 10 ohms, then use two 5 ohm resistors in a series.  Remember, when resistors are in a series:  R_Total = R1 + R2 + R3

A third quick solution is to give a circuit with 2 resistors in parallel that are double the target resistance.  e.g.  If your target is 10 ohms, use two 20 ohm resistors in parallel.  Remember, when resistors are in parallel:  1/R_Total = 1/R1 + 1/R2.  (ie 1/10 = 1/20 + 1/20 in the example I just gave.)

In short, just remember the two fundamental equations for combining resistors

Resistors in Series:

R_Total = R1 + R2 + R3

Resistors in Parallel:

1/R_Total = 1/R1 + 1/R2 + 1/R3