Question

A metal wire with specific resistance 1.84×10^-8 ohm metre and length 1 m has a resistance 26 ohm find the radius of the wire ?​

Answer 1

Step-by-step explanation:

R= rho× 1m/πr²

it will become too big so I will prefer u to solve this

Answer 2

Answer:

$\bigstar{\bold{Radius\:of\:wire=1.5\times 10^{-5}\:m}}$

Step-by-step explanation:

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

• Resistivity (ρ) = 1.84 × 10⁻⁸ Ω m
• Length (l) = 1 m
• Resistance = 26 Ω

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

• Radius of the wire

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

➾ First we have to find the area of the cross section of the wire

➾ We know that resistance of a conductor is given by,

    R = ρ l/A

➾ Substitute the data, we get the value of area,

    26 = 1.84 × 10⁻⁸ × 1/A

    26 A = 1.84 × 10⁻⁸

    A = 1.84 × 10⁻⁸/26

    A = 7.08 × 10⁻¹⁰ m²

➾ Hence area of the wire is 7.08 × 10⁻¹⁰ m²

➾ Now the radius of the wire is given by

    π r² = 7.08 × 10⁻¹⁰

➾ Substitute the data,

    3.14 × r² =  7.08 × 10⁻¹⁰

    r² =  7.08 × 10⁻¹⁰/3.14

    r² = 2.25 × 10⁻¹⁰

    r = √2.25 × 10⁻¹⁰

    r = 1.5 × 10⁻⁵ m

➾ Hence radius of the wire is  1.5 × 10⁻⁵ m

    $\boxed{\bold{Radius\:of\:wire=1.5\times 10^{-5}\:m}}$

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

➾ Resistance of a conductor is inversely proportional to the area of cross section. That is if area increases, resistance decreases and vice versa.

   $\sf{R\propto \dfrac{1}{A} }$

➾ Resistance of a conductor is directly proportional to the length of the conductor. That is if length increases, resistance increases and vice versa.

   $\sf{R\propto l}$

➾ Resistance of a conductor is given by,

    $\sf{R=\dfrac{\rho \:l}{A}}$