In the given circuit, the breakdown voltage of the Zener diode is $$3.0$$ V. What is the value of $$I_z$$?

This is a Zener regulator circuit.

step 1: check if Zener conducts

Zener breakdown voltage = 3 V
Supply = 10 V

So Zener will be in breakdown (active).

Thus voltage across A-B = 3 V

step 2: current through series resistor (1 kΩ)

Voltage drop across 1 kΩ:

$$10-3=7\text{ V}$$

$$I_{total}=\frac{7}{1000}=7\text{ mA}$$

step 3: current through load (2 kΩ)

Load is across A-B, so:

$$I_{load}=\frac{3}{2000}=1.5\text{ mA}$$

step 4: Zener current