147k views
1 vote
If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?

a) Aluminum, because it has a higher resistivity.

b) Copper, because it has a lower resistivity.

c) They have the same diameter.

d) Cannot be determined without additional information.

User TheSteed
by
6.9k points

1 Answer

2 votes

Final answer:

If aluminum and copper wires have the same resistance, then according to Ohm's Law, the resistance can be given by the formula: R = (ρ * L) / A, where A is the wire's cross-sectional area, L is its length, ρ is its resistivity, and R is its resistance.

Step-by-step explanation:

If aluminum and copper wires have the same resistance, then according to Ohm's Law, the resistance can be given by the formula: R = (ρ * L) / A, where A is the wire's cross-sectional area, L is its length, ρ is its resistivity, and R is its resistance. Since the resistance is the same for both wires, and the length is equal, we can compare their diameters.

The resistivity of aluminum is higher than that of copper, which means aluminum offers more resistance per unit length compared to copper. In order for aluminum to have the same resistance as copper, it needs to have a larger cross-sectional area (diameter). Therefore, the correct answer is a) Aluminum, because it has a higher resistivity.

User Mostafa Vatanpour
by
6.9k points