Question

A 2.0 m long wire has 1mm diameter and resistance of 7 Ohm.Calculate the resistivity of the material​

Answer 1

Given :-

Length of the wire = 2.0 m

Diameter of the wire = 1 mm

Resistance of the wire = 7 Ω

To Find :-

The resistivity of the material​.

Analysis :-

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

Firstly, find the radius by dividing the diameter by two.

in order to find the resistivity, substitute the values we got such that resistance is equal to resistivity multiplied by length divided by area.

Solution :-

We know that,

• a = Area
• d = Diameter
• r = Radius
• R = Resistance
• l = Length

Using the formula,

$\underline{\boxed{\sf Radius = \dfrac{Diameter}{2} }}$

Given that,

Diameter (d) = 1 mm

Substituting their values,

⇒ r = d/2

⇒ r = 1/2

⇒ r = 0.5 mm

Using the formula,

$\underline{\boxed{\sf Cross \ sectional \ area= \pi r^2}}$

Given that,

Radius (r) = 0.5 mm

Substituting their values,

⇒ 3.14 × 0.5²

⇒ 3.14 × 0.5 × 0.5

⇒ 3.14 × 0.25

⇒ 0.785 mm²

Using the formula,

$\underline{\boxed{\sf Resistivity=Resistance \times \dfrac{Area}{Length} }}$

Given that,

Resistivity (ρ) = 7 Ω

Area (a) = 0.785 mm²

Length (l) = 2000 mm

Substituting their values,

⇒ ρ = 7 × (0.785/2000)

⇒ ρ = 5.495/2000

⇒ ρ = 0.0027475 Ω - mm

⇒ ρ = 2.7475 × 10⁻⁶ Ω - m

Therefore, the resistivity of the material​ is 2.7475 × 10⁻⁶ Ω - m.

Answer 2

Answer :-

• Resistivity (ρ) = $\boxed{\tt{\red{2.75× 10^{-6}\:Ωm}}}$

Given :-

• Length of the wire ($\ell$) = 2m

• Diameter of wire (d) = 1mm

• Resistance of wire (R) = 7Ω

To find :-

• Resistivity of the material (ρ).

Formula used :-

• $\boxed{\sf{ρ = \dfrac{RA}{\ell}}}$

Here, A = Area of cross - section

Solution :-

• Radius (r) = $\sf{\dfrac{d}{2}}$ = 0.5mm = $\sf{5\times 10^{-4} m}$

• Area (A) = $\sf{\pi r²}$ = $\sf{\dfrac{22}{7} \times 25\times 10^{-8} m²}$

$\:$

➪ $\sf{ρ = \dfrac{RA}{\ell}}$

➪ $\sf{ρ = \dfrac{\cancel{7} \times \dfrac{\cancel{22}}{\cancel{7}} \times 25\times 10^{-8}}{\cancel{2}}}$

➪ $\sf{ρ = 11 \times 25\times 10^{-8}}$

➪ $\sf{ρ =}$ $\sf{\red{2.75\times 10^{-6}\:Ωm}}$