The value of power dissipated across the zener diode ($$V_z = 15$$ V) connected in the circuit as shown in the figure is $$x \times 10^{-1}$$ W.

The value of $$x$$ to the nearest integer is ________.

We need to find the value of $$x$$ to the nearest integer, which represents the power dissipated across the Zener diode in the given circuit.

1. Find the Total Current ($$I$$)

The Zener diode is connected in reverse bias parallel to the load resistor $$R_L$$. Since the input voltage ($22\text{ V}$) is greater than the Zener breakdown voltage ($$V_z = 15\text{ V}$$), the Zener diode operates in its breakdown region and maintains a constant voltage of $15\text{ V}$ across itself and the load.

The voltage drop across the series resistor $$R_s$$ is given by:

$$V_{Rs} = V_{in} - V_z = 22\text{ V} - 15\text{ V} = 7\text{ V}$$

Using Ohm's law, the total current $$I$$ flowing through the series resistor $$R_s = 35\ \Omega$$ is:

$$I = \frac{V_{Rs}}{R_s} = \frac{7}{35} = 0.2\text{ A}$$

2. Find the Load Current ($$I_1$$)

The voltage across the load resistor $$R_L = 90\ \Omega$$ is kept constant at $15\text{ V}$ by the Zener diode. The current $$I_1$$ flowing through the load is:

$$I_1 = \frac{V_z}{R_L} = \frac{15}{90} = \frac{1}{6}\text{ A} \approx 0.1667\text{ A}$$

3. Find the Zener Diode Current ($$I_2$$)

According to Kirchhoff's Current Law (KCL) at the junction:

$$I = I_1 + I_2$$

Solving for the Zener current $$I_2$$:

$$I_2 = I - I_1 = 0.2 - \frac{1}{6} = \frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30}\text{ A}$$

4. Calculate Power Dissipated across the Zener Diode ($$P_z$$)

The power dissipated by the Zener diode is given by the product of the voltage across it and the current flowing through it:

$$P_z = V_z \times I_2$$

$$P_z = 15 \times \frac{1}{30} = 0.5\text{ W}$$

We are given that the power dissipation is expressed in the form $$x \times 10^{-1}\text{ W}$$:

$$0.5\text{ W} = 5 \times 10^{-1}\text{ W}$$

Comparing this with the given expression, we find that $$x = 5$$.

Therefore, the value of $$x$$ to the nearest integer is 5.