Two resistors when connected together can produce maximum 25 ohm and minimum 6 ohm resistance. Find the The resistance of each resistor.

Explanation

Let we have two resistors of resistances `R_1 and R_2`.
The These produce minimum resistance when resistance connected in parallel and in parallel let their net resistance be `R_p`
`R_("minimum") = R_p = 6Omega` (given)
`implies 1/R_1 +1/R_2 =1/R_P`
`(R_1+R_2)/(R_1R_2) =1/6 " ....(1)`
These resistors produce maximum resistance when connected in series and set their net resistance be `R_S` .
`R_("minimum") = 25 Omega` (given)
`R_("minimum")= R_S=R_1 + R_2 = 25...(2)`
From (1),
`(25)/(R_1R_2) =1/6`
`R_1 R_2 = 150`
We know `(R_1-R_2)^2 = (R_1+R_2)^(2) - 4R_1R_2`
`(R_1-R_2)^2 = (25)^(2) - 4 (150)`
`(R_1-R_2)^(2) = 625 -600 = 25`
`R_1 -R_2 =sqrt(25) = 5 " "...(3)`
Adding (2) and (3) ,
`2 R_1 = 30`
`R_1 = 15 Omega`
Putting value of `R_1` in eqn. (3)
`15 - R_2 = 5`
`implies R_(2) = 15 - 5 = 10 Omega`