1. A coil is formed by winding 250 turns of insulated 16-gauge copper wire, that has a diameter d = 1.3 mm, in a single layer on a cylindrical form of radius 12 cm. What is the resistance of the coil? Neglect the thickness of the insulation and the resistivity of copper is ???? = 1.69 × 10−8 Ω ∙ m.

Respuesta :

Answer:

2.39 Ω

Explanation:

Given that

Number of winnings on the coil, = 250 turns

Radius if the copper wire, r(c) = 1.3/2 = 0.65 mm

Radius of single cylinder layer, R = 12 cm

Length of the cylinderical coil, L = 250 * 2π * 12 = 188.4 m

Resistivity of copper, ρ = 1.69*10^-8 Ωm

Area is πr(c)², which is

A = 3.142 * (0.65*10^-3)²

A = 3.142 * 4.225*10^-7

A = 1.33*10^-6 m²

The formula for resistance is given as

R = ρ.L/A, if we substitute, we have

R = (1.69*10^-8 * 188.4) / 1.33*10^-6

R = 3.18*10^-6 / 1.33*10^-6

R = 2.39 Ω.

Therefore, the resistance is 2.39 Ω

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