Question

the length of a conducting wire is 60 cm and radius is 0.5 mm. calculate the resistivity if the resistance is 20 ohm
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Answer 1

Answer:

$\bigstar{\bold{Resistivity=2.61 \times 10^{-5}\Omega\: m}}$

Explanation:

$\Large{\underline{\bf{Given:}}}$

• Length of the wire = 60 cm = 0.6 m
• Radius of the wire = 0.5 mm = 5 × 10⁻⁴ m
• Resistance = 20 Ω

$\Large{\underline{\bf{To\:Find:}}}$

• Resistivity

$\Large{\underline{\bf{Solution:}}}$

↦ First we have to find the area of cross section of the wire.

↦ Area of cross section = π r²

↦ Substitute the data,

   Area of cross section = 3.14 × (5 × 10⁻⁴)²

   Area of cross section = 3.14 × 25 × 10⁻⁸

   Area of cross section = 7.85 × 10⁻⁷

↦ Hence area of the cross section of the wire 7.85 × 10⁻⁷ m².

↦ Now resistivity is given by,

  R = ρ L/A

   where R = resistance

               ρ = resistivity

               L = length of conductor

               A = area of cross section

↦ Substituting the data,

    20 = ρ × 0.6/ 7.85 × 10⁻⁷

    764331.2 ρ = 20

    ρ = 20/764331.2

    ρ = 2.61 × 10⁻⁵ Ω m

↦ Hence resistivity of the conductor is 2.61 × 10⁻⁵ Ω m.

    $\boxed{\bold{Resistivity=2.61 \times 10^{-5}\Omega\: m}}$