The equivalent resistance of two resistors connected in series `6Omega` and their parallel equivalent resistance is `4/3Omega`. What are the value of resistance?

Options

A. `4Omega, 6Omega`
B. `8Omega, 1Omega`
C. `4Omega, 2Omega`
D. `6Omega, 2Omega`

Answer

C

Explanation

Let the value of resistance be `R_(1)` and `R_(2)` respectively. When `R_(1)` and `R_(2)` resistance are in series,
So, `R_(1)+R_(2)=6 Omega` ….(i)
(According to the question)
When `R_(1)` and `R_(2)` resistances are in parallel,
So, `(R_(1)R_(2))/(R_(1)+R_(2))=(4)/(3)Omega` .....(ii)
From the Eq. (i), we get
`(R_(1)R_(2))/(6)=(4)/(3)rArr R_(1)R_(2)=4xx2`
`R_(1)R_(2)=8 Omega` .....(iii)
We know that, `R_(1)-R_(2)=sqrt((R_(1)+R_(2))^(2)-4R_(1)R_(2))`
`R_(1)-R_(2)=sqrt(36-4xx8)`
`R_(1)-R_(2)=sqrt(4)`
`R_(1)-R_(2)=2Omega` .....(iv)
From the Eq. (i) and (iv), we get
`R_(1)=4Omega, R_(2)=2 Omega`