ELEG $21003$ Homework #$5(110$ points$)$

$1.(15$ points$)$ Calculate the current flowing through a $10$ F capacitor if the voltage

across its terminals is: $($a$)5$ V; $($b$)1152$ cos $120$; $($c$)4$

$2.(15$ points$)$ The current through a capacitor is given by $()=7$ sin $.$ If the

energy stored at t $=200$ ms is $3$ J$,$ what is the value of the capacitor?

$3.(15$ points$)$ Calculate the voltage across a $10$ nH inductor if the current into the $+$

reference terminal is: $($a$)5$ mA; $($b$)1152$ cos $120$; $($c$)4$

$4.(10$ points$)$ What is the maximum amount of energy that can be stored in a $5$ mH

inductor if the wire is rated for a maximum current of $1\mathrm{.}5$ A$?$

$5.(15$ points$)$ Let vs $=400$t $2$ V for t $>0$ and I L$(0)=0\mathrm{.}5$ A in the circuit. At t $=0\mathrm{.}4$ s$,$ find

the values of energy: $($a$)$ stored in the capacitor; $($b$)$ stored in the inductor; and $($c$)$

dissipated by the resistor since t $=0.$