## Suppose that you wish to fabricate a uniform wire out of1.15 g of copper. Assume the wire has aresistance R = 0.300 , and all ofthe copper i

Question

Suppose that you wish to fabricate a uniform wire out of1.15 g of copper. Assume the wire has aresistance R = 0.300 , and all ofthe copper is used.
(a) What will be the length of the wire?

(b) What will be the diameter of the wire?

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1 year 2021-09-04T00:39:33+00:00 1 Answers 4 views 0

(a) L = 149.2 cm

(b) d = 0.033 cm

Explanation:

Note that the resistivity of copper is

$$\rho = 1.72\times 10^{-8}~{\rm \Omega . m} = 1.72\times 10^{-6}~{\rm \Omega.cm}$$

and the mass density of copper is

$$d = 8.96~{\rm g/cm^3}$$

We will use the following formula to relate the resistance to other parameters

$$R = \frac{\rho L}{A} = \frac{\rho L}{\pi r^2}$$

If all the copper with 1.15 g is used, then

$$m = dV\\1.15 = 8.96 \times (L\pi r^2)\\L\pi r^2 = 0.128$$

Back to the resistance:

$$0.3 = \frac{1.72\times 10^{-6} L}{\pi r^2}\\L = \pi r^2 (1.74\times 10^5)\\L = \frac{0.128}{L}(1.74\times 10^5)\\L = 149.2~{\rm cm}$$

Then, the diameter is

$$149.2\times \pi r^2 = 0.128\\r = 0.0165~{\rm cm}\\d = 2r = 0.033~{\rm cm}$$