Question

A copper wire has a diameter of 0.5 mm and resistivity of 1.6×10⁻⁸ Ω⋅m. Calculate the length of this wire to make the resistance 1000 ohms.

(a) 160 m
(b) 320 m
(c) 480 m
(d) 640 m

Answer 1

To calculate the length of the copper wire to make the resistance 1000 ohms, use the formula resistance = (resistivity * length) / (cross-sectional area). Given the diameter and resistivity of the wire, rearrange the formula to solve for the length.

Step-by-step explanation:

To calculate the length of the copper wire to make the resistance 1000 ohms, we can use the formula: resistance = (resistivity * length) / (cross-sectional area)

Given: diameter = 0.5 mm (radius = 0.25 mm = 0.00025 m), resistivity = 1.6x10^-8 Ω⋅m, and resistance = 1000 ohms

Using the equation for the cross-sectional area of a wire, A = π * r^2, we can find the area: A = π * (0.00025 m)^2 = 1.9635x10^-7 m^2

Rearranging the formula, we get: length = (resistance * A) / resistivity = (1000 ohms * 1.9635x10^-7 m^2) / 1.6x10^-8 Ω⋅m = 1.22656 m

Therefore, the length of the copper wire needed to make the resistance 1000 ohms is approximately 1.23 m.