Three unequal resistor in parallel are equivalent to a resistance `1Omega` If two of them are in the ratio 1:2 and if no resistance value is fractional the largest of the three resistance in ohm is

Options

A. `10Omega`
B. `8 Omega`
C. `15Omega`
D. `6 Omega`

Answer

D

Explanation

`R_(eq)=1 Omega`
`(1)/(R_eq)=(1)/(R_1)+(1)/(R_2)+(1)/(R_3)`
`R_3= 2R_2`
`(1)/(R_eq)=(1)/(R_1)+(1)/(R_2)+(1)/(2R_2)`
`(1)/(R_eq)=(1)/(R_1)+(3)/(2R_2)rArr (1)/(1)=(1)/( R) +(3)/(3R_2)`
Verifying with options
`(1) (1)/(1)=(1)/(R_1)+(3)/(2R_2)`
`R_(1)=1 Omega R_2 = 3Omega alpha`
`(1)/(1)=(1)/(1)+(3)/(2(3))=(1)/(1)+(3)/(4)=(7)/(4)`
`(2) R_1=2 Omega R_2 =3 Omeag`
`(1)/(1) =(1)/(2) +(1)/(3)+(1)/(R_3)`
`(1)/(1)=(5)/(6)+(1)/(R_3)`
`1-(5)/(6)=(1)/(R_3)`
`(1)/(6)=(1)/(R_3)`
`R_3 = 6 Omega`.
`6 Omega ` is the highest resistance.