You can pay a lot of money for fancy connecting cables between your audio/video equipment components. Some of the more expensive ones use silver wire rather than copper. Calculate the difference in resistance between a silver and a copper cable with the same 12-gauge wire with diameter of 2.05 mm and length of 3 m hence total length = 6m). Use ρ_Cu = 1.7 × 10^-8Ω/m and ρ_Ag = 1.6 × 10^-8 Ω/m. Unfortunately, or fortunately, there are many other factors that go into making an interconnect cable than simple resistance considerations.)

Question

Quizplus · Accepted Answer

Using the given formula, we can calculate the resistance of the copper cable first:
ρS1U1B1CuS1U1B0 = 1.7 × 10S1U1P1-8 S1S1P0Ω/m

ρCopper = (1.7 × 10S1U1P1-8) x (6) = 1.02 × 10S1U1P1-7S1S1P0 Ω

Now, we can calculate the resistance of the silver cable using the given formula:
ρS1U1B1AgS1U1B0 = 1.6 × 10S1U1P1-8S1S1P0 Ω/m.

ρSilver = (1.6 × 10S1U1P1-8) x (6) = 9.6 × 10S1U1P1-8S1S1P0 Ω

To find the difference in resistance, we subtract the resistance of the copper cable from the resistance of the silver cable:
ρSilver - ρCopper = (9.6 × 10S1U1P1-8) - (1.02 × 10S1U1P1-7) = -0.03 × 10S1U1P1-7S1S1P0 Ω

We can see that the resistance of the silver cable is actually lower than that of the copper cable, but only by a very small amount. Therefore, the difference in resistance between the two cables is:
-0.03 × 10S1U1P1-7S1S1P0 Ω

Which, after rounding to the nearest significant figure, gives us 1.8 × 10S1U1P1-3S1S1P0 Ω. Therefore, the best choice is B) with the explanation that the difference in resistance between the two cables is very small, and therefore, not a significant factor in the selection of an interconnect cable.

You Can Pay a Lot of Money for Fancy Connecting