The equivalent resistance of a series combination of two resistors is '9 Omega' and the equivalent resistance of a parallel combination of the same two resistors is 2 Omega. Find the resistances of the resistors.

The equivalent resistance of a series combination of two resistors is

1.	The equivalent resistance of a series combination of two resistors is '9 Omega' and the equivalent resistance of a parallel combination of the same two resistors is 2 Omega. Find the resistances of the resistors.
Answer» Solution : Suppose two unknown resistances are x and y. When the resistors are connected in parallel `(xy)/(x +y) = 2Omega` andwhen they are connected in series `x +y = 9 Omega` So, `(xy)/9 = 2 :.Xy = 18 Omega` Now, From`x +y = 9 , y = 9-x` `:. x (9-x) =18` `:. 9 x -x^2 =18` `:. x^2 -9x + 18 = 0` `:. x- 6X - 3x + 18 =0` `:. x(x-6)-3 (x-6)=0` `:.(x -3) (x -6) =0` `:. x =3 Omega or x = 6Omega` Hence `y = 9-x =9-3 = 6 Omega or y =9 -6 = 3OMEGA` THUS, ` x=3 Omega and y = 6Omega or x =6 Omega and y = 3Omega`