A) \[1:\frac{1}{2}:\frac{1}{6}\]
B) \[\frac{1}{2}:\frac{2}{5}:\frac{4}{3}\]
C) \[3:3:4\]
D) \[3:4:3\]
Correct Answer: D
Solution :
: In parallel, potential difference is same. Let the length of wires be\[2l,6l\]and\[18l\]. Let the radii of wires be r, 2r and 3r \[\therefore \]\[R=\frac{\rho {{l}_{1}}}{\pi r_{1}^{2}}=\frac{\rho }{\pi }\frac{2l}{{{r}^{2}}}\] \[{{R}_{2}}=\frac{\rho }{\pi }\frac{{{l}_{2}}}{r_{2}^{2}}=\frac{\rho }{\pi }\frac{6l}{{{(2r)}^{2}}}=\frac{\rho }{\pi }\frac{6l}{4{{r}^{2}}}\] \[{{R}_{3}}=\frac{\rho }{\pi }\frac{{{l}_{3}}}{r_{2}^{2}}=\frac{\rho }{\pi }\frac{18l}{{{(3r)}^{2}}}=\frac{\rho }{\pi }\frac{2l}{{{r}^{2}}}\] \[\therefore \]\[{{l}_{1}}:{{l}_{2}}:{{l}_{3}}=\frac{V}{{{R}_{1}}}:\frac{V}{{{R}_{2}}}:\frac{V}{{{R}_{3}}}\] \[=\frac{V\times \pi {{r}^{2}}}{\rho \times 2l}:\frac{V\times \pi \times 4{{r}^{2}}}{6l}:\frac{V\times \pi {{r}^{2}}}{\rho \times 2l}\] \[=1:\frac{4}{3}:1=3:4:3\]
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