Ex$.10$: In the Figure shown below, $V_S$ is an unregulated voltage that varies between $6$ V and $7$ V while the Zener diode voltage is $V_Z=5V.$ The load resistor $R_L$ can have a value from $100$ to prop $($i$.$e$.,$ open circuit$).$ Also you can take $I_{Z(\text{m}\text{i}\text{n})}$~$=0A.$

a$)$ Find the maximum value of $R_1$ so that the load voltage $V_L$ would be still kept constant at $5$ V for all values of $R_L$ and $V_S.$

b$)$ Provide a symbolic expression for the maximum power dissipated by the Zener diode.

c$)$ Determine the minimum value of $R_1$ so that the power dissipated by the Zener diode does never exceeds $1$ W for all values of $R_L$ and $V_S.$

Sol. :