Problem $7$: UMF $8\mathrm{.}18$

$8\mathrm{.}18$ Determine the complex power, apparent power, average power absorbed$,$ reactive power, and power factor $($including whether it is leading or lagging$)$ for a load circuit whose voltage and current at its input terminals are given by:

$($a$)$ v$($t$)=110$cos$(60$r $-60$ deg$)$ V$,$ i$($t$)=4$cos$(60$r $-25$ deg$)/$

$($b$)$ v$($t$)=12$cos$(1000$r $+30$ deg$)*$ V

i$($t$)=0\mathrm{.}4$cos$(1000$t $-15$ deg$)/$

$($c$)$ v$($t$)=-10$cos$(3000$t $+10$ deg$)$ V$,$ i$($t$)=0\mathrm{.}5$sin$(3000$t $-5$ deg$)/$

$($d$)$ Vrms $240/0$ V$.$ Irms $=0\mathrm{.}8/50$ A$.$

$($e$)$ Vrms $6/20$ V$.$ Irms $=255/15$ mA$.$

$($f$)$ Vrms $18/40$ V$.$ Irms$1/-50$ A$.$

A