Question

when two resistances R1 and R2 are connected in parallel the net resistance is 3ohm when connected in series it is 16ohm.find the values of R1 and R2

Answer 1

r1+r2=16
1/r1+1/r2=1/3
(r1+r2)/r1*r2=1/3
48=r1*r2
r1=48/r2 ........(1)
also as r1+r2=16
from (1)
48/r2+r2=16
let r2=x
48+x2=16*x
x2-16x+48=0
x2-4x-12x+48=0
x(x-4)-12(x-4)=0
(x-4)(x-12)=0
either r2=4ohm or 12 ohm
so r1 =12ohm or 4 ohm respectively...