A Zener of breakdown voltage $$V_Z = 8$$ V and maximum Zener current, $$I_{ZM} = 10$$ mA is subjected to an input voltage $$V_i = 10$$ V with series resistance $$R = 100$$ $$\Omega$$. In the given circuit $$R_L$$ represents the variable load resistance. The ratio of maximum and minimum value of $$R_L$$ is ______.

Total series current: $$I_s = \frac{V_i - V_Z}{R} = \frac{10 - 8}{100} = 0.02\ \text{A} = 20\ \text{mA}$$

For maximum load resistance, Zener current is maximized ($$I_Z = I_{ZM} = 10\ \text{mA}$$):

$$(I_L)_{\text{min}} = I_s - I_{ZM} = 20 - 10 = 10\ \text{mA}$$

$$(R_L)_{\text{max}} = \frac{V_Z}{(I_L)_{\text{min}}} = \frac{8}{10 \times 10^{-3}} = 800\ \Omega$$

For minimum load resistance, Zener current is minimized ($$I_Z = 0\ \text{mA}$$):

$$(I_L)_{\text{max}} = I_s - 0 = 20\ \text{mA}$$

$$(R_L)_{\text{min}} = \frac{V_Z}{(I_L)_{\text{max}}} = \frac{8}{20 \times 10^{-3}} = 400\ \Omega$$

$$\frac{(R_L)_{\text{max}}}{(R_L)_{\text{min}}} = \frac{800}{400} = 2$$