Question

Suppose you have three resistors of 20 Ω, 50 Ω and 100 Ω. What minimum and maximum resistance can you obtain from these resistors?

Answer 1

We can obtain maximum resistance when all the resistors are connected in series.
So, maximum resistance,
$R_{\max }=\left(20+50+100\right)\mathrm{\Omega }=170\mathrm{\Omega }$
The minimum resistance will be obtained when all the resistors are connected in parallel
So, minimum resistance,

$R_{\min }=\frac{1}{{\displaystyle \frac{1}{20}}+{\displaystyle \frac{1}{50}}+{\displaystyle \frac{1}{100}}}=\frac{100}{8}=12.5\mathrm{\Omega }$