JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 27)
Eight copper wire of length $$l$$ and diameter $$d$$ are joined in parallel to form a single composite conductor of resistance $$R$$. If a single copper wire of length $$2 l$$ have the same resistance $$(R)$$ then its diameter will be ____________ d.
Answer
4
Explanation
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$$RAB = R$$
$$R = {1 \over 8}$$ (Resistance of one wire)
$$ = {1 \over 8}\rho {l \over {\pi {{{d^2}} \over 4}}} = {{\rho l} \over {2\pi {d^2}}}$$
Resistance of copper wire of length $$2l$$ and diameter $$x = R$$
$$\rho {{2l} \over {\pi {{{x^2}} \over 4}}} = R$$
$${{8\rho l} \over {\pi {x^2}}} = {{\rho l} \over {2\pi {d^2}}}$$
$$16{d^2} = {x^2}$$
$$x = 4d$$
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