To avoid using two auxiliary power sources, Enzo came up with the idea of generating $5$ V power from a single $12$ V source. Recently, his colleagues had designed the zener diode linear regulator illustrated below. Enzo wants this circuit to regulate an output voltage Vo of $5$ V to power a load with a current that may vary from $0$ to $100$ mA$,$ considering the consumption of the microcontroller and other components included in his project. Help Enzo assess the viability of this circuit:

a$.$ Determine the equivalent resistance RL of the circuit based on the regulated voltage and maximum current consumption. $[5$ pts$]$

b$.$ Check whether the circuit can regulate the voltage Vo at $5$ V for the entire load current range IL$.[15$ pts$]$

c$.$ Verify whether the zener diode used $($BZX$55$C$),$ with a maximum operating power of $500$ mW$,$ is suitable for the application when the circuit's consumption is minimal $($IL $=0$ A$).[15$ pts$]$

d$.$ If the zener diode cannot handle it$,$ suggest alternatives for Enzo to solve the problem. $[5$ pts$]$