Question

resistance of a metal wire of length 1m in 26ohm at 20°C. If the diameter of the wire is 0.3mm, what will be the resistivity of the metal at that temperature ​

Answer 1

Answer:

$\bigstar{\bold{Resistivity=1.8369\times 10^{-6}\Omega\:m}}$

Explanation:

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

• Length of the wire = 1 m
• Resistance = 26 Ω
• Temperature = 20° C
• Diameter of the wire = 0.3 mm = 3 × 10⁻⁴ m

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

• The resistivity of the wire

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

➻ Here we are given the resistance, diameter and length of the wire.

➻ We have to find the resistivity at the specific temperature

➻ We know by the formula,

    $\sf{R=\dfrac{\rho \:l}{A} }$

   where R is the resistance

   ρ is the resistivity

   l is the length

   A is the area of cross section

➻ First we have to find the area of cross section of the give wire

    Area of cross section = π r²

➻ Substitute the data,

    Area of cross section = 3.14 × (3 × 10⁻⁴/2)²

    Area of cross section = 3.14 × (1.5 × 10⁻⁴)²

    Area of cross section = 3.14 × 2.25 × 10⁻⁸

    Area of cross section = 7.065 × 10⁻⁸ m²

➻ Now substitute the value in the above formula,

    $\sf{26=\dfrac{\rho \times 1}{7.065\times 10^{-8} }}$

   ρ = 26 × 7.065 × 10⁻⁸

   ρ = 1.8369 × 10⁻⁶ Ω m

➻ Hence resistivity of the wire is 1.8369 × 10⁻⁶ Ω m

    $\boxed{\bold{Resistivity=1.8369\times 10^{-6}\Omega\:m}}$

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

➥ Resistance of a conductor is directly proportional to its length. If length of the conductor increases, resistance increases and vice versa.

    $\sf{R\propto l}$

➥ Resistance is inversely proportional to the area of cross section. If area increases, resistance decreases and vice versa.

    $\sf{R\propto \dfrac{1}{L} }$