$($b$)$ Given v$(0)=0$V$,$i$(0)=0$A and u$($t$)$ is a unit step function, determine i$($t$)$ of the circuit in Figure $2\mathrm{.}2$ by using s$-$domain analysis.

$(12$ Marks$)$

$3.($a$)$ The circuit in Figure $3\mathrm{.}1$ is designed such that the $50$ Hz current source delivers maximum power to the load modeled by the resistor R and inductor L $.$ Find the value of the resistor R and inductor L for maximum power to be delivered to the load. Hence, find the maximum power absorbed by the load.