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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 force experienced by it is zero

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4:3

2:5

5:3

3:1

answer is C.

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Detailed Solution

if wires are connected parallel current in them is inversely proportional to resistance

$I_{1} : i_{2 :} i_{3} = \frac{!}{R_{1}} : \frac{1}{R_{2}} : \frac{1}{R_{3}} = \frac{1}{3} : \frac{1}{4} : \frac{1}{5} = 20 : 12 : 15$

force on the middle wire from other two if x and y are the distances from them

$\frac{{Î¼}_{0} 20 Ã 15}{2 Ï x} = \frac{{Î¼}_{0} 12 Ã 15}{2 Ï y} \frac{x}{y} = \frac{12}{20} = \frac{3}{5}$

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