Five $\frac{1}{6}\Omega$ resistors can produce maximum resistance of :

To get maximum resistance, the resistance should be connected in series.

As the circuit's current flows sequentially through each resistor in a series connection, the total resistance equals the sum of the individual resistances.

The total resistance in a series combination can be calculated as:

${\mathrm{R}}_{\mathrm{eq}}={\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3+......$

The total resistance when five resistors are linked in series will be given by:

$R_{eq}= \frac{1}{6}+ \frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}= \frac{5}{6}\Omega$.

Therefore, five $\frac{1}{6}\Omega$ resistors can produce maximum resistance of  $\frac{5}{6}\Omega$ With a series connection.