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. 4
B. 6
C. 5
D. 12

Answer

B

Explanation

Here, `(R_(1))/(R_(2))=(1)/(2)orR_(2)=2R_(1)`
The equivalent resistance of parallel combination
`(1)/(R)=(1)/(R_(1))+(1)/(R_(2))+(1)/(R_(3))=(1)/(R_(1))+(1)/(2R_(1))+(1)/(R_(3))=(3)/(2R_(1))+(1)/(R_(3))`
or `(1)/(R_(3))=(1)/(1)-(3)/(2R_(1))=1-(3)/(2R_(1))`
or `1=R_(3)-(3)/(2)(R_(3))/(R_(1))orR_(3)=1+(3)/(2)(R_(3))/(R_(1))`
Since no resistance is in fraction, therefore minimum value of `(R_(3))/(R_(1))=(2)/(3)`
`therefore R_(3)=1+(3)/(2)xx(2)/(3)=2OmegaandR_(1)=3Omega`
The maximum resistance value is
`R_(2)=2R_(1)=2xx3=6Omega`