Answer
a.) 131.684 Ohm and 29.6485 Ohm
b.) 367.55 W and 1632.5 W
Work Step by Step
Start by calculating the resistance of each configuration in terms of variables $R_1$ and $R_2$
Series: $ R = R1 + R2$
Parallel: $R = R1*R2/(R1 + R2)$
Series will have lowest power since it has highest resistance of the configurations
Parallel will have the highest power since it has the lowest resistance
Series: $ 300 = (220)^2 / (R1 + R2)$
Parallel: $2000 = 220^2 * (R1 + R2) /( R1*R2)$
2 unknowns and 2 equations
Solving for R1 and R2 in calculator gives: R1 = 131.684, R2 = 29.6485
Now use the equation $ P = V^2 /R$ to calculate the other powers
R1 : $P = 220^2 / 131.68 = 367.55 W$
R2: $P = 220^2 / 29.6485 = 1632.5W$
