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  • The masses of the three wires of copper are in the ratio 5 : 3 : 1 and their lengths are in the ratio 1 : 3 : 5. The ratio of their electrical resistance is:Opti

The masses of the three wires of copper are in the ratio 5 : 3 : 1 and their lengths are in the ratio 1 : 3 : 5. The ratio of their electrical resistance is:

Option: 1

5:3:1


Option: 2

\sqrt{125}:15:1


Option: 3

1:15:125


Option: 4

1:3:5


Answers (1)

best_answer

Given, l_1=1 \mathrm{k}, l_2=3 \mathrm{k}, l_3=5 \mathrm{k} \text { and } \mathrm{m}_1=5 \mathrm{~m}, \mathrm{~m}_2=3 \mathrm{~m}, \mathrm{~m}_3=1 \mathrm{~m}

Resistance \mathrm{R}=\frac{\rho l}{\mathrm{~A}}

Where, \rho is resistivity of the material of conductor.

So, \mathrm{R}_1: \mathrm{R}_2: \mathrm{R}_3=\frac{l_1}{\mathrm{~A}_1}: \frac{l_2}{\mathrm{~A}_2}: \frac{l_3}{\mathrm{~A}_3}=\frac{l_1^2}{\mathrm{~V}_1}: \frac{l_2^2}{\mathrm{~V}_2}: \frac{l_3^2}{\mathrm{~V}_3}

=\frac{l_1^2}{\mathrm{~m}_1}: \frac{l_2^2}{\mathrm{~m}_2}: \frac{l_3^2}{\mathrm{~m}_3}=\frac{1}{5}: \frac{9}{3}: \frac{25}{1}=1: 15: 125

Posted by

SANGALDEEP SINGH

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