For the adjacent circuit, determine the average power supplied by the source $V_S$ and the average power dissipated in resistor R$.$ Note: According to passive sign convention the average power supplied by the AC source is a negative quantity, and the power dissipated by resistor R is a positive quantity. Be sure to include units. $($Hint: Ideal inductors do not dissipate power.$)(9$ points total.$)$

$P_{\text{s}\text{o}\text{u}\text{r}\text{c}\text{e}}=q,(6$ points. $1$ point for sign using the passive sign convention.$)$

$P_R=.(3$ points. $1$ point for sign using the passive sign convention.$)$