$(4$ marks$)$

$($b$)$ A Zener Diode regulator shown in Fig Q$3($b$)$ is used to give an average DC output voltage of $6$ V across a maximum load $($R$\_($L$))$ of $480\backslash$Omega $.$ After the voltage regulation a peak$-$ to$-$peak ripple voltage of $0\mathrm{.}16$ V remains at the output. The input voltage V$\_($i$)$ has an average value of $17$ V and a peak$-$topeak ripple voltage designated as $\backslash$Delta V$\_($i$).$ The value of the series resistor R is $600\backslash$Omega and the diode used is rated at $6$ V $,$ has an internal resistance of $25\backslash$Omega $,$ requires a minimum current of $2\mathrm{.}5$ mA and can handle a maximum current of $40$ mA $.$ Calculate:

$($i$)$ the maximum current in the load R$\_($L$)$V$\_($i max $)$ V$\_($i min $)$