DC currrent question ALL ANSWERS IN SI UNITS! 1. You need to send DC current 100

Question

DC currrent question

ALL ANSWERS IN SI UNITS! 1. You need to send DC current 1000 km through a wire. You have gold, aluminum and copper as options. Use Wikipedia elemental data, or the values in the textbook tables for the values you need- identify your sources. a. Cost is not a concern. If all three wires were made with the same diameter, which material would produce the lowest power losses over the 1000km distance? Show your numbers. b. If you wanted to send 1000 Amperes of current through the wire using the best material from part a, what would be the smallest diameter wire that could be used? (Hint- maximum practical current densities are approximately 6 Ampere-mm^-2) c. How much power would be dissipated in the 1000km of wire?

Explanation / Answer

Resistivity of gold = 2.44* 10^(-8) ohm-m

Resistivity of aluminium = 2.82* 10^(-8) ohm-m

Resistivity of copper =1.68* 10^(-8) ohm-m

Resistance = resistivity * (L/A)

1) L/A is same for all wires

So, losses are minimu if resistance is minimum

For minimum resistance resistivity should be minimum

Lowest power loss would be in copper wire

2) J = I/A

6 * 10^6 = 1000/A (for minimum area maximum density aloowed is used)

A_min = 1.66 * 10^(-4) m^2

(3.14 * d^2)/4 = 1.66 * 10^(-4)

d_min = 0.014m = 1.4 cm

3) Power dissipated = I^2 * R

R = [1.68 * 10^(-8)   * 1000*1000]/1.66 * 10^(-4)

R = 101.2 ohm

P lost = 1000^2 * 101.2 = 101.2 MW

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.