the voltage will be in the form Vmaxsin(wt).

can someone please check my work to see if it all checks out its really important i do well on this.

so i know that for maximum power transfer the Zth has to be equal to the Zload

here i know that Zth will be sqrt(R^2 +(w^2)(L^2) which is equal to Zload

so then Zload must be equal to Rload

the current going through the circuit will be

I = (Vmax/Zth + Zload)

and P = (Irms^2)(Rload) = (Rload/2)(Vmax/(Zth+Zload))^2

if this is not correct please any hints towards the answer would be appreciated