Answer:
(a) L = 128.75 m
(b) L = 182.56 m
(c) L = 114.28 m
(d) Mass of Gold = 7.68 kg = 7680 gram
(e) Cost of Gold Wire = $ 307040
Explanation:
The resistance of the wire is given as:
R = ρL/A
where,
R = Resistance
ρ = resistivity
L = Length
A = cross-sectional area
(a)
For Gold Wire:
ρ = 2.44 x 10⁻⁸ Ω.m
A = πd²/4 = π(2 x 10⁻³ m)²/4 = 3.14 x 10⁻⁶ m²
R = 1 Ω
Therefore,
1 Ω = (2.44 x 10⁻⁸ Ω.m)L/(3.14 x 10⁻⁶ m²)
L = (1 Ω)(3.14 x 10⁻⁶ m²)/(2.44 x 10⁻⁸ Ω.m)
<u>L = 128.75 m</u>
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(b)
For Copper Wire:
ρ = 1.72 x 10⁻⁸ Ω.m
A = πd²/4 = π(2 x 10⁻³ m)²/4 = 3.14 x 10⁻⁶ m²
R = 1 Ω
Therefore,
1 Ω = (1.72 x 10⁻⁸ Ω.m)L/(3.14 x 10⁻⁶ m²)
L = (1 Ω)(3.14 x 10⁻⁶ m²)/(1.72 x 10⁻⁸ Ω.m)
<u>L = 182.56 m</u>
<u></u>
(c)
For Aluminum Wire:
ρ = 2.75 x 10⁻⁸ Ω.m
A = πd²/4 = π(2 x 10⁻³ m)²/4 = 3.14 x 10⁻⁶ m²
R = 1 Ω
Therefore,
1 Ω = (2.75 x 10⁻⁸ Ω.m)L/(3.14 x 10⁻⁶ m²)
L = (1 Ω)(3.14 x 10⁻⁶ m²)/(2.75 x 10⁻⁸ Ω.m)
<u>L = 114.28 m</u>
<u></u>
(d)
Density = Mass/Volume
Mass = (Density)(Volume)
Volume of Gold = AL = (3.14 x 10⁻⁶ m²)(128.75 m) = 4.04 x 10⁻⁴ m³
Therefore,
Mass of Gold = (1.9 x 10⁴ kg/m³)(4.04 x 10⁻⁴ m³)
<u>Mass of Gold = 7.68 kg = 7680 gram</u>
<u></u>
(e)
Cost of Gold Wire = (Unit Price of Gold)(Mass of Gold)
Cost of Gold Wire = ($ 40/gram)(7680 grams)
<u>Cost of Gold Wire = $ 307040</u>
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