Task $5$

$(15$ pts$)$

Consider the circuit as shown in Fig. Q$5.$ Nodes a and $b$ are the output to be connected to a load impedance.

Fig. Q$5.$ AC circuit in time domain

a$)$ Find the complex values of $11$ and the reactance associated with C$1.$

$[4$ pts$]$

b$)$ Based on your answer to part $($a$)$ of this question, find the Thevenin equivalent model for the above circuit.

$($Hint: The reactance associated with C$1$ is too large. There should be no current flowing through C$1.$ The circuit should be readily reduced by Thevenin$-$to$-$Norton or Norton$-$to$-$Thevenin conversion.$)$

$[9$ pts$]$

c$)$ Calculate the load impedance to be connected to the output of the above circuit such that the power transfer to the load is maximum. You may assume that the load is complex.

$[2$ pts$]$