Solve the following using Laplace transforms: consider an LRC$-$series circuit with L$=0\mathrm{.}5$ H$,$ R$=20$ ohms, C$=0\mathrm{.}001$ Farads. Assume both the current across the resistor and the charge on the capacitor are equal to zero at t$=0,$ and also that at this time an external voltage E$($t$)=100$sin$60$t is applied. find the steady$-$state current, writing it in the form I$($t$)=$ Asin$($wt$+$phi$).$ What is the maximum charge on the capacitor?