A three$-$phase delta$-$connected ac voltage controller is used to control the speed of a $3-,5hp,208V,60Hz$ induction motor. At full$-$load output $(5hp,208V),$ the power factor is $0\mathrm{.}85$ lagging, and the efficiency is $90\%.$

$($a$)$ Draw the circuit.

$($b$)$ Determine the input KVA for full$-$load output condition.

$($c$)$ What is the range of the firing angle for the full$-$load condition.

$($d$)$ Determine the $($i$)$ voltage and $($ii$)$ current ratings of the thyristors for full$-$load condition.

$($e$)$ If the power factor is $0\mathrm{.}8($lagging$),$ for a firing angle of $60,$ draw qualitatively the waveform of the motor current and motor voltage for one phase.