The power that will be taken when 100 V is applied to the two coils is 60.6 W.
(the given options are wrong).
How to calculate the power taken?
The power that will be taken when 100 V is applied to the two coils connected in series is calculated by applying the following formula as shown below.
The resistance and reactance of coil A;
Z₁ = 100 V / 8 A
Z₁ = 12.5 Ω
120 = (8)² x R₁
R₁ = 120 / 64
R₁ = 1.875 Ω,
The effective reactance;
X₁ = √ (12.5² - 1.875²)
X₁ = 12.36 Ω
The resistance and reactance of coil B;
Z₂ = 100 V / 10 A
Z₂ = 10 Ω
120 = (10)² x R₂
R₂ = 120 /100
R₂ = 1.2 Ω
The effective reactance;
X₂ = √ (10² - 1.2²)
X₂ = 9.93 Ω
When the resistors are connected in series, we will have
R = R₁ + R₂
R = 1.875 Ω + 1.2 Ω
R = 3.075 Ω
X = 12.36 Ω + 9.93 Ω
X = 22.29 Ω
Z = √ (3.075² + 22.29²)
Z = 22.5 Ω
The power taken is;
P = I²R
I = 100 V / 22.5Ω,
I = 4.44 A
P = (4.44²) x 3.075
P = 60.6 W
The closest option is C.