Find the current through the circuit elements. Next evaluate the voltage across each element. Finally, the instantaneous power associated with an element will be the product of the current and voltage at that time.
Find the extreme value by setting the derivative with respect to R to zero. Calculus enthusiasts should prove that this yields a maximum value by evaluating the second derviative...
a)Looking at the power dissipated by the resistor, we want Pmax/Pmin = (Imax/Imin)2 = (Zmax/Zmin)2 = 5.
Solve for L in
5 = [R2+XL2] / R2.
b) Set up a resistive voltage divider and repeat the calculation above.
Evaluate the voltage phasor for each circuit element and combine appropriately to find the voltage across combinations of elements.