1. Maximum equivalent resistance

To get the maximum resistance using all 10 resistors of $10\,\Omega$ each, we connect them all in series.

$R_{\max} = 10 + 10 + \cdots + 10 \quad (10\text{ times})$

$R_{\max} = 10 \times 10 = 100\,\Omega$

2. Minimum equivalent resistance

To get the minimum resistance using all 10 resistors, we connect them all in parallel.

For 10 identical resistors of resistance $10\,\Omega$ in parallel,

$R_{\min} = \frac{10}{10} = 1\,\Omega$

3. Required ratio

$\frac{R_{\max}}{R_{\min}} = \frac{100}{1} = 100$

Hence, the required ratio is:

$\boxed{100}$