A wire of radius 5 x 10⁻⁴ m is needed to prepare a coil of resistance 40 Ω. The resistivity of the material of the wire is 3.14x10⁻⁷ Ωm. Calculate the length of the wire.

100 m

Explanation:

From the question,

R = Lρ/A Equation 1

Where R = resistance of the wire, L = length of the wire, ρ = resistivity of the wire, A = cross sectional area of the wire.

But,

A = πr² Equation 2

Where r = radius of the wire.

Substitute equation 2 into equation 1

R = Lρ/πr²

Make L the subject of the equation

L = Rπr²/ρ Equation 3

Given: R = 40 Ω, r = 5×10⁻⁴ m, ρ = 3.14×10⁻⁷ Ωm

Constant: π = 3.14

Substitute these values into equation 3

L = [40×3.14×( 5×10⁻⁴)²]/ (3.14×10⁻⁷)

L = 40×3.14×25×10⁻⁸/(3.14×10⁻⁷)

L = 100 m

Hence the length of the wire is 100 m

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