Find an expression for current flowing through `R_(g)` . Which potential is higher `V_(A)` or `V_(B)` ?

Explanation

From ABDA,
`l_(1) + l_(g) xx 10 - 2l_(2) = 0" "…..(i)`
From BCDB,
`2l_(1) - 2lg - l_(2) - l_(1) - 10l_(g) = 0`
`rArr " " 2l_(1) + l_(2) + l_(g) - 4 = 0 " " …..(ii)`
From ADCA ,
`2l_(2) + l_(2) + l_(g) - 4 = 0 " "......(iii)`
Multiplying by 2. in Eq. (i) , we get
`rArr " " 2l_(1) + 20l_(g) - 4l_(2) = 0 " ".....(iv)`
Eq. (i) -Eq. (iii) , we get
`3l_(2) - 33l_(2) = 0`
`rArr " " 3 xx 11 l_(g) + l_(g) - 4 = 0`
`rArr " " 34 l_(g) =4 `
`rArr " " l_(g) = (4)/(34)A = (2)/(17)A`