QUESTION FOUR

$($a$)$ Consider the single phase uncontrolled diode rectifier diagram below

Derive the value using the above circuit

$($i$)$ The average value of the load voltage $V_L$ is $V_{de}=0\mathrm{.}318V_m[2]$

$($ii$)$ The Rme value of the output voltage $V_{\text{r}\text{m}\text{e}}=0\mathrm{.}5V_m[2]$

$($iii$)$ Form factor $FF=1\mathrm{.}57[1]$

$($iv$)$ Ripple factor $RF=1\mathrm{.}21[1]$

$($v$)$ Transformer utilization factor $($TUF$)=0\mathrm{.}286$

$[2]$

$($b$)$ Consider the three$-$phase half wave controlled rectifier, draw the equivalent circuit diagram

$[2]$

$($c$)$ Explain the operations of the above circuit and draw the wave form characteristics

$[2]$

$($d$)$ Derive and show the following using the above circuit

$($i$)V_{dc}=0\mathrm{.}8727V_{m}cos$

$($ii$)V_m=0\mathrm{.}84V_m$

$[4]$

$[4]$