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Two coils connected in series have a resistance of 36 ohm and when connected in parallel have a resistance of 8ohm. Find resistance of each coil​

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Answer:

Explanation:

Remark

Two resistances in series has the form of

Rs= C1 + C2

Two resistances is parallel has the form of

Rp = (C1 *C2)/(C1 + C2)

The plan is to first of all find C1*C2 and use this information and C1 + C2 to find the individual resistances.

Givens

Rs = 36 ohms

Rp = 8 ohms

Solution

Rp = C1 * C2/(C1 + C2)

Rp = 8 ohms

C1 + C2 = 36 ohms

8 =    C1*C2 / 36                          Multiply by 36

8* 36 = C1*C2

C1*C2 = 288

Use Rs to solve for C1

  • C1 + C2 = 36
  • C1 = 36 - C2

(36 - C2) * C2 = 288

36*C2 - C2^2 =288                    Multiply by - 1

-36C2 + C2^2 = -288                 Add 288 to both sides

C2^2 - 36C2 + 288= 0               Factor this equation

(C2 - 12)(C2 - 24)

C2 - 12 = 0

C2 = 12

C2 - 24 = 0

C2 = 24

C2 = 24 or

C2 = 12

C1 = 36 - C2

C1 = 36 - 24 = 12

C1 = 36 - 12  = 24

Answer

C1 = 12 ohms or 24 ohms

C2 = 24 ohms or 12 ohms

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