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When a voltage of 100 V at 50 Hz is applied to a choking coil A, the current taken is 8A and the power is 120 W, when applied to a coil B, the current is 10 A and the power is 120 W.

What power will be taken when 100 V is applied to the two coils connected in series?
A. 4737 W
B. 140 W
C. 70 W
D. 1454 W

User Sardoan
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8.1k points

1 Answer

2 votes

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.

User Jemiloii
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8.5k points