Three long straight wires are connected parallel to each other across a battery of negligible internal resistance. The ratio of their resistances are 3 :

Q: 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

c (c) The wires are in parallel and ratio of their resistances are $3 : 4 : 5$, Hence currents in wires are in the ratio $\frac{1}{3}:\frac{1}{4}:\frac{1}{5}$ ${i_1} = \frac{k}{3}$ ${i_{_2}} = \frac{k}{4}$ ${i_3} = \frac{k}{5}$ Force between top and middle wire ${F_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2{i_1}{i_2}}}{{{r_1}}}$ $ = \frac{{{\mu _0}}}{{4\pi }} \times \frac{{2\left( {\frac{1}{3}} \right)\,\left( {\frac{1}{4}} \right)\,{k^2}}}{{{r_1}}}$. Force between bottom and middle wire ${F_2} = \frac{{{\mu _0}}}{{4\pi }}\frac{{\left( {\frac{1}{4}} \right)\;\left( {\frac{1}{5}} \right){k^2}}}{{{r_2}}}$. As the forces are equal and opposite so ${F_1} = {F_2} \Rightarrow \frac{{{r_1}}}{{{r_2}}} = \frac{5}{3}$.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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

A$4 : 3$
B$3 : 1$
C$5 : 3$
D$2 : 3$

Diffcult

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

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