Question

When a voltage of 100 V at 50 Hz is applied to a choking coil A, the current taken is 8 A and the power is 120 W. When applied to a coil B, the current is 10 A and the power is 500 W. What current and power will be taken when 100 V is applied to the two coils connected in series ?

Answer 1

Z₁ = 100/8 = 12.5 Ω ; P = I₂ . R₁ or 120 = 8² × R₁ ; R₁ = 15/8 Ω

X₁ = √(Z²₁ - R²₁) = √(12.5² - (15/8)²⁾ = 12.36Ω

Z₂ = 100/10 = 10 Ω ; 500 = 10² × R₂ or R₂ = 5 Ω

X₂ = √(10² - 5²) = 8.66Ω

With Joined in Series 

R = R₁ + R₂ = (15/8) + 5 = 55/9 Ω; X = 12.36 + 8.66 = 21.02 Ω

Z = √((55/8)² + (21.02)²) =Ω I = 100/22.1 = 4.52 A, P = I²R = 4.522 × 55/8 = 140W