If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire

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Physics Calantha 5 years 2021-07-31T13:26:23+00:00 2021-07-31T13:26:23+00:00 1 Answers 11 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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linhdan · Answer 1 · 2021-07-31T13:28:11+00:00

linhdan

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2021-07-31T13:28:11+00:00 July 31, 2021 at 1:28 pm

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Explanation:

The resistance of a wire is given by the formula as follows :

$R=\rho \dfrac{l}{A}$

l is length of wire

A is area of cross section, $A=\pi r^2$

Since, r=d/2, d = diameter

$A=\pi \dfrac{d^2}{4}$

It is given in the problem that the resistance of two aluminum wires is same.

$R_1=R_2\\\\\rho\dfrac{L_1}{\pi d_1^2/4}=\rho\dfrac{L_2}{\pi d_2^2/4}\\\\\dfrac{L_1}{L_2}=\dfrac{d_1^2}{d_2^2}$

We have, L₁=2L₂

So,

$\dfrac{2L_2}{L_2}=\dfrac{d_1^2}{d_2^2}\\\\\dfrac{d_1^2}{d_2^2}=2\\\\\dfrac{d_1}{d_2}=\sqrt{2}$

So, the ratio of the diameter of the longer wire to the diameter of the shorter wire is $\sqrt2:1$