Question

Show how would you connect three resistors of 6 ohm each so that the equivalent resistance of combination is
a) 9 ohm
b)6 ohm

Answer 1

R1, R2, R3  each of  6 Ω

a)   Equivalent resistance of  9 Ω
       9 - 6 = 3  ohms...  
         3 = 6 / 2....
     so    R1  +   R2 R3 / (R2 + R3)  = 9 Ω
     we connect  R3 and R2 in parallel.   Then we connect R1 in series with them.

b)  we use one of the resistances only to get 6 Ω.  We cannot make a series or parallel combination of 3 resistances to get  6 Ω again.