Question

when two resistors are connected in sereies are connected in series, their effective resistance is 80 Ohm. When they are connected in parallel, their effective resistance is 20 Ohm. What are the values of the two resistances?

Answer 1

Let R1 and R2 be the two resistances. When they are in parallel, resultant resistance Rp is given by

1/Rp = 1/R1 + 1/R2

Rp = R1R2/(R1 + R2)

2 = R1R2/(R1 + R2)

2(R1 + R2) = R1R2

When they are in series effective resistance 

Rs = R1 + R2

9 = R1 + R2 ⇒ R2 = 9 - R1

2 x 9 = R1 R2

         = R1 (9 - R1)

         = 9R1 - R12.

18 = 9R1 - R12.

R12 - 9R1 + 18 = 0

Solve this quadratic equation. You will get 

R1 = (9 ± √(81 - 4 x 1 x 18))/2

     = (9 ± √9)/2

     =  (9 ± 3)/2

R1 = 3 ohm or 6 ohm

If R1 = 3 ohm, R2 = 6 ohm and vice versa.