Question

Determine the resistance of a copper wire having a length 1km and diameter of a 0.5mm

Answer 1

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Answer 2

Answer:

87.64 Ω

Explanation:

Given:

Length of wire, L = 1 km = 1000 m

Diameter of cross section of wire, D = 0.5 mm = 5 * 10⁻¹ mm = 5 * 10⁻² cm

or, D = 5 * 10⁻⁴ m

Radius of cross section of wire, r = D/2 = 2.5 * 10⁻⁴ m

So, area of cross section of wire, A = πr² = 3.14 * 2.5 * 10⁻⁴ * 2.5 * 10⁻⁴

= 3.14 * 6.25 * 10⁻⁸

= 19.625 * 10⁻⁸ m²

We know that resistivity of copper wire at room temperature, ρ = 1.72 * 10⁻⁸ Ωm

To find: Resistivity , R of copper wire = ?

Solution:

We know that

$R = \rho \dfrac{L}{A}\\\\\\\implies R = \dfrac{1.72 \times 10^{-8} \times 1000}{19.625 \times 10^{-8}}\\\\\\= \dfrac{172 \times 1000 \times 1000}{100 \times 19625}\\\\\\= \dfrac{1720000}{19625}\\\\\\= \dfrac{13760}{157}\\\\\\= \boxed{\boxed{\underline{\boxed{\bold{87.64 \; \Ohm}}}}}$