Question

You are given three resistors of magnitude 3 Ω each. You can join them either in a series or in a parallel combination. How will you arrange them so that the equivalent resistance would become:

1. maximum
2. minimum

(Your answer must be accompanied by proper mathematical calculations)

Answer 1

(a) For maximum resistance, connect all three resistors in series.

Rs = 3 + 3 + 3 = 9 Ω

So the maximum equivalent resistance is 9 Ω.

(b) For minimum resistance, connect all three resistors in parallel.

`1/R_p = 1/3 + 1/3 + 1/3 = 3/3 = 1`

`R_p = 1 Ω`

So the minimum equivalent resistance is 1 Ω.

Therefore, the series combination gives maximum resistance and the parallel combination gives minimum resistance.