Six resistances each of v ale r=`6Omega` are connected between points A,B and C as shown in the figure if `R_(1),R_(2)` and `R_(3)` are the net resistances between A and B, between B and C and between A and C respectively, the `R_(1):R_(2):R_(3)` will be equal to

Options

A. `6:3:2`
B. `1:2:3`
C. `5:4:3`
D. `4:3:2`

Answer

3

Explanation

In the branch AC, three resistors each of resistance r are in parallel, so their equivalent resistance is `(r)/(3)`.
In the branch BC, two resistors each of resistance r are in parallel
so their equivalent resistance is `(r)/(2)`
The equivalent circuit of the given circuit is as shown in adjacent figure.
Net resistance between A and B is

`R_(1)=(((r)/(3)+(r)/(2))xxr)/((r)/(3)+(r)/(2)+r)=( 5)/(11)r`
Net resistance between B and C
`R_(2)=((r+(4)/(3))xx(r)/(2))/(r+(r)/(3)+(r)/(2))=(4)/(11)r`
Net resistance between A and C is
`R_(3)=((r+(r)/(2))xx(r)/(3))/(r+(r)/(2)+(r)/(3))=(3)/(11)r`
`therefore R_(1):R_(2):R_(3)=(5)/(11)r:(4)/(11)r:(3)/(11)r`
`=5:4:3`