Question

With 4 identical resistances number of different combinations is

Answer 1

If selections from the population are allowed from 3 different resistors, there are

3 choices of 1 resistor

3 choices of two resistors in series

3 choices of two resistors in parallel

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Then, if only all three resistors may be used, there are

1 choice of three in parallel

1 choice of three in series

3 choices of two in series, one in parallel end to end.

3 choices of two in parallel the remainder in series.

This makes a total of eight ways of arranging all three.

There are another nine ways of choosing one or two of three resistors:

a grand total of 17 discrete results if the resistors are all different values.

Now we consider the smaller universe where all resistors are equal, and we only permit one resultant resistance value:

1 choice of 1 resistor = R

1 choice of 2 resistors in series = 2R

1 choice of 2 resistors in parallel = 1/2 R

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Then if all three must be used

1 choice of 3 in parallel = R/3

1 choice of 3 in series = 3R

1 choice of 2 in parallel and 1 in series = 1.5 R

1 choice of 2 in series with 1 in parallel end to end = 2/3 R