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
(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
