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. `5`
C. `6`
D. `10`

Answer

c

Explanation

Given, `(R_(1))/(R_(2)) =(1)/(2) or R_(2) = 2R_(1)`
The equivalent resistance of parallel combination
is `(1)/(R ) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3))`
`(1)/(R_(1)) + (1)/(2R_(2)) + (1)/(R_(3))= (3)/(2R_(1)) + (1)/(R_(3))`
or `(1)/(R_(3)) = (1)/(R )-(3)/(2R_(1)) = (1)/(1)- (3)/(2R_(1))`
or `1 = R_(3) = (3R_(3))/(2R_(1))`
`R_(3) = (3R_(3))/(2R_(1))`
Since no resistance value is fractional, hence minimum value of `(R_(1))/(R_(2)) = (2)/(3)`
So `R_(2) = 1+ (3)/(2)xx(2)/(3) = 1+1 = 2 Omega`
and `R_(1) = (3R_(3))/(2) = (3xx2)/(2) = 3 Omega`
`:.` Maximum resistance value is of
`R_(2) = 2R_(1) = 2 xx 3 = 6 Omega`