Three long straight wires are connected parallel to each other across a battery of negligible internal resistance. The ratio of their resistances are `3:4:5`. What is the ratio of distances of middle wire from the others if the net forces experienced by it is zero.

Explanation

The wires are in parallelt and ratio of their resistances are `3:4:5`, Hence currents in wires are in the ratio `(1)/(3):(1)/(4):(1)/(5)`

`i_(1)=(k)/(3),i_(2)=(k)/(4),i_(3)=(k)/(5)`
Force between top and middle wire is
`F_(1)=(mu_(0))/(4pi).(2i_(1)i_(2))/(r_(1))=(mu_(0))/(4pi)xx(2((1)/(3))((1)/(4))k^(3))/(r_(1))`
Force between bottom and middle wire
`F_(2)=(mu_(0))/(4pi)(((1)/(4))((1)/(5))k^(2))/(r_(2))`
As the forces are equal and opposite so `F_(1)=F_(2)implies(r_(1))/(r_(2))=(5)/(3)`