Question

Calculate the ratio of the resistance of 11.0 mm of aluminum wire 2.2 mm in diameter, to 28.0 mm of copper wire 1.8 mm in diameter. The resistivity of copper is 1.68 × 10⁻⁸ Ω ⋅ m and the resistivity of aluminum is 2.65×10⁻⁸Ω⋅m

Answer 1

To calculate the ratio of the resistance of the aluminum wire to the copper wire, find the resistance of each wire using their length, diameter, and resistivity. Then, divide the resistance of the aluminum wire by the resistance of the copper wire.

Step-by-step explanation:

To calculate the ratio of the resistance of the aluminum wire to the copper wire, we need to find the resistance of each wire first. The resistance of a wire can be calculated using the formula R = (ρ * L) / A, where R is resistance, ρ is resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.

For the aluminum wire, the length is 11.0 mm and the diameter is 2.2 mm. We can use these values to calculate the cross-sectional area (A = π * (d/2)^2) and then use the resistivity of aluminum (2.65 × 10⁻⁸ Ω ⋅ m) to find the resistance.

Similarly, for the copper wire, the length is 28.0 mm and the diameter is 1.8 mm. We can calculate the cross-sectional area and then use the resistivity of copper (1.68 × 10⁻⁸ Ω ⋅ m) to find the resistance.

Once we have the resistance values, we can calculate the ratio by dividing the resistance of the aluminum wire by the resistance of the copper wire.