Two resistances are in the ratio of 1.4. If these are connected in parallel, their total resistance becomes `16Omega` . Find the value of each resistance.

Explanation

Let we have two resistors of resistances `R_1 and R_2`
Let `R_1=R`
`[ :. R_1 : R_2= 1:4]`
`R_2 = 4 R`
Their net resistance in parallel `=R_P = 16Omega`
`:. 1/R_P = 1/R_1 +1/R_2`
`implies 1/(16)=1/R+1/(4R)`
`implies 1/16 =(4+1)/(4R) = 5/(4R)`
`implies 4R = 16 xx5 = 80`
`implies R= (80)/4 = 20Omega`
So `R_1 =R =20Omega`
`R_2 = 4 R = 4 xx 20 =80 Omega`