Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6 V. If the unregulated input voltage varies between 10 V to 16 V, then what is the maximum Zener current?

The constant load current ($$I_L$$) passing through the load resistor $$R_L$$ when the Zener diode is in its breakdown region ($$V_Z = 6\ \text{V}$$):

$$I_L = \frac{V_Z}{R_L} = \frac{6\ \text{V}}{4\ \text{k}\Omega} = 1.5\ \text{mA}$$

The maximum source current ($$I_{S,\text{max}}$$) flows when the unregulated input voltage reaches its peak value ($$V_{\text{in}} = 16\ \text{V}$$):

$$I_{S,\text{max}} = \frac{V_{\text{in,max}} - V_Z}{R_S} = \frac{16\ \text{V} - 6\ \text{V}}{2\ \text{k}\Omega} = \frac{10\ \text{V}}{2\ \text{k}\Omega} = 5\ \text{mA}$$

Applying Kirchhoff's Current Law at the junction node ($$I_S = I_Z + I_L$$), the maximum Zener current ($$I_{Z,\text{max}}$$):

$$I_{Z,\text{max}} = I_{S,\text{max}} - I_L = 5\ \text{mA} - 1.5\ \text{mA} = 3.5\ \text{mA}$$