Question $2(25$ marks$)$

A base current of $\backslash (80\backslash$mu $\backslash$mathrm$\{$~A$\}\backslash )$ is applied to a silicon bipolar junction transistor $($BJT$),$ as shown in Figure $2.$ The value of the variable resistor Rc is adjusted so that the collector current is $8$ mA and the voltage drop across Rc is $8$ V $.$ The voltage between the collector and base terminals is $0\mathrm{.}3$ V $.$ At room temperature, $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$BE$\}\}=0\mathrm{.}7\backslash$mathrm$\{$~V$\}\backslash ).$

$($a$)$ Calculate the value of the variable resistor $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$C$\}\}\backslash ).$

$($b$)$ Calculate $\backslash (\backslash$alpha $\backslash )$ and $\backslash (\backslash$beta $\backslash )$ for the transistor.

$($c$)$ Find $\backslash ($ V$\_\{$B B$\}\backslash )$ and Vcc$.$

$($d$)$ Find the minimum value of Rc$,$ which makes the transistor go into the active region.