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Question

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 + R2 from 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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