$4.$ For the circuit shown, $Vcc=15V,R_E=470,R_2=,r_e=26m\frac{V}{I_E},r_o=,Rs=0,Rc=2\mathrm{.}2k,R_L=12k,Cs=2\mathrm{.}2F,C_E=100F,CC=1F$ and $=100,$ silicon transistor.

a$.$ Determine the value of $R_1$ to have $I_{CQ}=2mA$

b$.$ Calculate $V_{CQ}$ and $V_{\text{C}\text{E}\text{Q}}$

c$.$ Calculate input and output impedances with and without $C_E$

d$.$ Calculate the critical frequency due to $C_E$

e$.$ Determine the $AC$ voltage gain $V\frac{o}{V}$i with and without $C_E.$