Exercise $1$

Figure $1$

e$($t$)=400*\backslash$sqrt$(2)*$cos$(\backslash$omega $*$t$)=400*\backslash$sqrt$(2)*$cos$(100*\backslash$pi $*$t$)$ is associated to E$\_()$ its RMS complex

value. Z$\_(1)=0,5+$j$*0,5,$ Z$\_(2)=0,1+$j$*0,3,$ Z$\_(3)=0,2+$j$*0,6$

Z$\_(1)$ is capacitive or inductive $?$ Justify your answer.

Give E$\_()$

Calculate Z$\_($eq$1)\_(),$ give numerical application

Calculate I$\_(3)\_(),$ justify your answer

Calculate U$\_(3)\_(),$ justify your answer.

Calculate I$\_(1)\_()$ and deduce i$\_(1)($t$)$

Calculate $()/($bar$)($Z$)\_($gq$)$ the impedance of the load

Calculate Active Power consume by Z$\_($eq$)\_()$

Calculate Reactive Power consume by Z$\_($eq $).7$

In the figure $2,$ give the value of the Capacitor in order to have for the whole circuit

cos$\backslash$phi $-1,$ justify your answer.

In these conditions, give the value of $|$I$\_($C$)\_(|),$ comment this value.