Question

A wire of length 88cm and diameter 0.4mm has a resistance of 6ohm . calculate the specific resistance of the material of wire​

Answer 1

Answer:

The required specific resistance of the wire​ is approximately 0.86 × 10⁻⁶ Ω-m

Explanation:

Given :

• length of the wire = 88 cm
• diameter of the wire = 0.4 mm
• resistance of the wire = 6 Ω

To find :

the specific resistance of the material of wire

Solution :

The resistance of a wire is given by,

 $\dag \boxed{\tt R=\dfrac{\rho l}{A}}$

where

ρ denotes the specific resistance

l denotes the length

A denotes the area of cross section

⇒ length = 88 cm

length = 0.88 m

⇒ diameter = 0.4 mm

radius = 0.4/2 = 0.2 mm

radius = 0.2 × 10⁻³ m

⇒ Area of cross section = πr²

Area = (22/7) × (0.2 × 10⁻³)²

Area = (22/7) × 0.04 × 10⁻⁶

Area =  0.88/7 × 10⁻⁶ m²

Substitute the values,

$\sf 6=\dfrac{\rho \times 0.88}{\dfrac{0.88}{7} \times 10^{-6}} \\\\ \sf \rho= 6 \times \dfrac{1}{7} \times 10^{-6} \\\\ \sf \rho \simeq 0.86 \times 10^{-6} \ \Omega - m$

∴ The specific resistance of the given wire​ is approximately 0.86 × 10⁻⁶ Ω-m