Question

A coil is made of 150 turns of copper wire wound on a cylindrical core. If the mean radius of the turns is 6.5 mm and the diameter of the wire is 0.4 mm, calculate the resistance of the coil!

Answer 1

Answer:

0.84 Ω

Explanation:

r = mean radius of the turn = 6.5 mm

n = number of turns of copper wire = 150

Total length of wire containing all the turns is given as

L = 2πnr

L =  2 (3.14)(150) (6.5)

L = 6123 mm

L = 6.123 m

d = diameter of the wire = 0.4 mm = 0.4 x 10⁻³ m

Area of cross-section of the wire is given as

A = (0.25) πd²

A = (0.25) (3.14) (0.4 x 10⁻³)²

A = 1.256 x 10⁻⁷ m²

ρ = resistivity of copper = 1.72 x 10⁻⁸ Ω-m

Resistance of the coil is given as

$R = \frac{\rho L}{A}$

$R = \frac{(1.72\times 10^{-8}) (6.123))}{(1.256\times 10^{-7}))}$

R = 0.84 Ω