When two resistors are connectedin series, their effective resistancei

1.	When two resistors are connectedin series, their effective resistanceis 80 Ω. When they are connectedin parallel, their effective resistanceis 20 Ω. What are the values of thetwo resistances?
Answer» Let R1and R2be the two resistances. When they are in parallel, resultant resistance Rp is given by 1/Rp= 1/R1+ 1/R2Rp= R1R2/(R1+ R2)2 =R1R2/(R1+ R2)2(R1+ R2) =R1R2 When they are in series effective resistance Rs= R1+ R29 = R1+ R2⇒ R2= 9 - R1 2 x 9 = R1R2 = 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)/2R1 = 3 ohm or 6 ohm If R1 = 3 ohm, R2 = 6 ohm and vice versa. wrong answer answer is 40ohm

When two resistors are connectedin series, their effective resistanceis 80 Ω. When they are connectedin parallel, their effective resistanceis 20 Ω. What are the values of thetwo resistances?

Answer»

Let R1and R2be the two resistances. When they are in parallel, resultant resistance Rp is given by

1/Rp= 1/R1+ 1/R2Rp= R1R2/(R1+ R2)2 =R1R2/(R1+ R2)2(R1+ R2) =R1R2

When they are in series effective resistance

Rs= R1+ R29 = R1+ R2⇒ R2= 9 - R1

2 x 9 = R1R2 = 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)/2R1 = 3 ohm or 6 ohm

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

wrong answer answer is 40ohm