Answer:
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
