Two coils have a combined resistance of 25 ohms, when connected in series and a resistance of 4 ohms when connected in parallel. What is the resistance of each coil?

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Solution

Let the resistances be R₁ and R₂.

According to question,

R₁ + R₂ = 25 …………….(1)

1/R₁ + 1/R₂ = 1/4 ----------(2)

=> (R₁ + R₂)/R₁R₂ = 1/4

put R₁ + R₂from equation 1

25/R₁R₂= 1/4

R₁R₂ = 4 × 25

=> R₁R₂ = 100 …………..(3)

Using (1) and (3),

(R₁ – R₂)² = (R₁ + R₂)² – 4R₁R₂

=> (R₁ – R₂)² = 625 – 4(100)

=> R₁ – R₂ = 15 ………….(4)

Solving (1) and (4) we get,
R₁ + R₂ = 25
R₁ – R₂ = 15
____________

2R₁= 40

R₁= 20

putting this in any one of the Equation (both give the same answer)
putting in (1)

R₂= 25-20
So

R₁ = 20 Ω

R₂ = 5 Ω

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