$($a$)[3$ marks$]$Give the three assumptions made for a transformer to be considered ideal

$($b$)[4$ marks$]$Derive the equivalent circuit $($T$-$network$)$ for the transformer in Fig. Q$3$

$($c$)[5$ marks$]$Determine the input impedance seen by the source in Fig. Q$3$

$($d$)[4$ marks$]$Determine the circuit impedance seen by the load in Fig. Q$3$

$($e$)[3$ marks$]$Determine the primary circuit current in Fig. Q$3,$in sinusoidal form

$($f$)[1$ marks$]$Determine the power factor of the circuit in Fig. Q$3$

Fig. Q$3$