3 resistance each of 2 of which are equal are connected in series then the effective resistance is 30ohm when these resistance connected in parallel effective resistance is 3ohm find the individual resistance?

Let the three resistances be R_1, R _{2 ,} and R_3.

Let the effective Resistance in series be R_s, and in parallel be R_p.

Given:    R_s = 30 ohm and R_p =3 ohm.

We know that   R_s = R₁ + R₂ +R₃  = 30 ……. Equation (1)

                            ……Equation (2)

If two of the three resistances are equal, then R₁ =R₂ =R (say).

From (1);

                 R+R+R₃ =30

              R₃ = 30 – 2R …… Equation (3)

From (2);

                  

                   

                    3(2R₃+R)           = RR₃

                                6R₃ +3R           =RR₃

Using (3);      6(30-2R) + 3R =R (30-2R)

                       180-12R+3R   =30R-2R²

                                   2R² – 39R +180=0

Solving the quadratic equation,

                          

                              

Taking  one possible value, we get

                             

R₁=12 , R₂ =12  and R₃=6           since R₃=30-2R

 

Taking the other possible value, we get

                            

R₁=7.5 , R₂=7.5  and R₃ = 15      since R₃=30-2R