Question

What is minnimum resistance you can get using 5 resistors of 1/5 ohm each?

Answer 1

Minimum resistance ia achieved when resistors are connected in parallel.

Resistance of each resistor, r = 1/5 ohm

Number of resistor = 5

Let the effective resistance when connected in parallel = R'
$\frac{1}{ R'} = \frac{1}{ \frac{1}{5} } + \frac{1}{ \frac{1}{5} } + \frac{1}{ \frac{1}{5} } + \frac{1}{ \frac{1}{5} } + \frac{1}{ \frac{1}{5} } \\ \\ \frac{1}{ R'} = 5 + 5 + 5 + 5 + 5 \\ \\ \frac{1}{ R'} = 25 \\ \\ R' = \frac{1}{25}$

So minimum effective resistance is 1/25 ohm