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?

Asked by farzul hazan C.S | 13th Jul, 2013, 11:27: AM

Expert Answer:

Let the three resistances be R1, R 2 , and R3.

Let the effective Resistance in series be Rs, and in parallel be Rp.

Given:    Rs = 30 ohm and Rp =3 ohm.

We know that   Rs = 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

Answered by  | 13th Jul, 2013, 08:43: PM

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