Question

The length of copper wire is 100 meter. It's radius is 1mm. Resistivity of pure copper is 1.72 X 10^-8 ohm meter. Calculate it's resistance.​

Answer 1

Answer :-

Resistance of the wire is 0.55 Ω .

Explanation :-

We have :-

→ Length of the wire = 100 m

→ Radius of the wire = 1 mm = 10⁻³ m

→ Resistivity = 1.72 × 10⁻⁸ Ωm

______________________________

Firstly, let's calculate the area of cross section of the wire.

⇒ A = πr²

⇒ A = 3.14 × 10⁻³ × 10⁻³

⇒ A = 3.14 × 10⁻⁶ m²

Now, we know that :-

R = ρl/A

Substituting values, we get :-

⇒ R = [1.72 × 10⁻⁸ × 100]/[3.14 × 10⁻⁶]

⇒ R = [172 × 10⁻⁸]/[3.14 × 10⁻⁶]

⇒ R = [1.72 × 10⁻⁶]/[3.14 × 10⁻⁶]

⇒ R = 1.72/3.14

⇒ R = 0.55 Ω

Answer 2

Given:-

• The length of copper wire is 100 meter. It's radius is 1mm.

• Resistivity of pure copper is $1.72 \times 10^{-8}$ ohm meter.

To Find:-

• It's resistance.

Formula Used:-

• ${\boxed{\bf{Area\:of\:Cross\: Section=\pi r^2}}}$

• ${\boxed{\bf{Resistance=ρ \dfrac{l}{A}}}}$

Solution:-

Firstly,

$\sf :\implies\:Area\:of\:Cross\: Section=\pi r^2$

• Here, r = 1mm = $\bf 10^{-3}$

$\sf :\implies\:Area\:of\:Cross\: Section=\dfrac{22}{7}\times 10^{-3}\times 10^{-3}$

$\sf :\implies\:Area\:of\:Cross\: Section=\dfrac{22}{7}\times 10^{-6}$

$\bf :\implies\:Area\:of\:Cross\: Section=3.14\times 10^{-6}\:m^2$

Now,

$\sf :\implies\:Resistance=ρ \dfrac{l}{A}$

$\sf :\implies\:Resistance=1.72 \times 10^{-8}\times \dfrac{100}{3.14\times 10^{-6}}$

$\sf :\implies\:Resistance= \dfrac{1.72\times10^{-8}}{3.14\times 10^{-8}}$

$\sf :\implies\:Resistance= \dfrac{1.72}{3.14}$

$\sf :\implies\:Resistance= \dfrac{172}{314}$

$\sf :\implies\:Resistance= \dfrac{86}{157}$

$\bf :\implies\:Resistance= 0.54\:ohm$

Hence, The Resistance is 0.54 ohm.

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