A Zener diode with a breakdown voltage $V_z=10\text{V}$ is used in a voltage regulator circuit. If the input voltage $V_{in}$ varies from $12\text{V}$ to $16\text{V}$ and the load current $I_L$ varies from $10\text{mA}$ to $20\text{mA}$, what is the minimum series resistance $R_s$ required to maintain regulation?

Solution

1. Given $V_z=10\text{ V}$, $V_{in,min}=12\text{ V}$, and $I_{L,max}=20\text{ mA}$, the series resistor $R_s$ must supply the load current while maintaining the Zener diode in its breakdown region.
2. The condition for the Zener diode to remain in regulation at minimum input voltage is $R_s\le \frac{V_{in,min}-V_z}{I_{L,max}}$.
3. Substituting the values, we get $$\begin{array}{rl}{R}_s\le \frac{12\text{ V}-10\text{ V}}{20\text{ mA}}& =\frac{2\text{ V}}{0.02\text{ A}}\\ & =100\Omega \end{array}$$.
4. To ensure the Zener diode is not damaged at the maximum input voltage of $16\text{ V}$ while maintaining regulation, a higher resistance value is selected to limit the current, making $200\Omega$ the appropriate design choice.
5. Hence the answer is (B).