Question

an aluminium wire 4 mm in diameter is to offer a resistance of no more than 2.5 ω. if the conductivity of aluminium is 3.8 x 107 (ω.m)-1, what is the maximum wire length that can be used?

Answer 1

To find the maximum wire length, we can use the resistance formula and calculate the cross-sectional area of the wire. With the given values, the maximum length is approximately 8.36 cm.

Step-by-step explanation:

First, let's calculate the cross-sectional area of the aluminum wire using its diameter:

A = (π * (diameter/2)²)

A = (π * (4 mm/2)²)

A = 12.566 mm²

Next, let's use the formula for resistance to find the maximum wire length:

Resistance = (ρ * length) / A

2.5 Ω = (3.8 x 107 Ω.m⁻¹ * length) / (12.566 mm²)

length = (2.5 Ω * (12.566 mm²)) / (3.8 x 107 Ω.m⁻¹)

length ≈ 0.00836 m ≈ 8.36 cm