CBSE Class 10 Answered

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