Suppose you wish to fabricate a uniform wire out of 1.30 g of copper. If the wire is to have a resistance R = 0.360 N, and ifall the copper is to be used, find the following.(a) What will be the length of the wire?Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake inyour calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m(b) What will be the diameter of the wire?X mm

Answered: Suppose you wish to fabricate a uniform…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Suppose you wish to fabricate a uniform wire out of 1.30 g of copper. If the wire is to have a resistance R = 0.360 N, and if
all the copper is to be used, find the following.
(a) What will be the length of the wire?
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in
your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m
(b) What will be the diameter of the wire?
X mm

Expert Solution

Step 1

Given:

The mass of the copper is m=1.30 g.

The resistance is $R = 0.360 Ω$ .

Also,

The density of copper is d=8.92X10³ kg/m³.

The resistivity of copper is $ρ = 1.7 \times 10^{- 8} Ω‐m$ .

Part (a)

The expression for length of the wire is:

$\begin{array}{rcl} R & = & \frac{ρ L}{A} \\ R & = & \frac{ρ L}{\frac{V}{L}} \\ R & = & \frac{ρ L^{2}}{\frac{m}{d}} \\ L & = & \sqrt{\frac{R m}{ρ d}} \\ L & = & \sqrt{\frac{(0.360 Ω) (1.30 g× \frac{1 kg}{1000 g})}{(1.7 \times 10^{- 8} Ω‐m) (8.92 \times 10^{3} \frac{kg}{m^{3}})}} \\ L & = & 1.75 m \end{array}$

Thus, the length of the wire is 1.75 m.

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