$10\mathrm{.}8$ The source voltage in the circuit shown is $\backslash (80\backslash$cos $250$ t $\backslash$mathrm$\{$~V$\}\backslash ).$

a$.$ What impedance should be connected across terminals $\backslash ($ a $\backslash )$ and $\backslash ($ b $\backslash )$ for maximum average power transfer?

b$.$ What is the average power transferred to the impedance in $($a$)?$

c$.$ Assume that the load is restricted to pure resistance. What size resistor connected across a and $\backslash ($ b $\backslash )$ will result in the maximum average power transferred?

d$.$ What is the average power transferred to the resistor in $($c$)?$