Part A. The formula relating electric power, voltage and current is:
P = I V
I = P / V
I = 4,100 W / 240 V
I = 17.08333 A
I = 17.08 A
Part B. The maximum amount of current an electrical wire can conduct is measure in terms of Ampacity. For a 12-gauge wire the Ampacity is greater than 20 A. Therefore the answer to this is “Yes”.
Part C. The formula for resistance is:
R = V / I
R = 240 V / 17.08 A
R = 14.05 Ω
Part D. The cost per hour is:
(11 cents / kwh) (4.1 kw) = 45.1 cents / hr