Question

A wire is 1m long, 0.2mm in diameter and has resistance of 10Ω. Calculate its resistivity.

Answer 1

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Understanding the concept -

★ This question says that the length of a wire is 1 metre and it is 0.2mm in diameter and has resistance of 10 ohms. We have to calculate it's resistivity.

Given that -

★ Length is 1 m in length.

★ 0.2mm in diameter.

★ Resistance of 10Ω.

To find -

★ Resistivity

Solution -

★ Resistivity = ${\sf{\rho = \: \: 3.14 \times 10^{-7}}}$ Ω mm

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Using concept -

★ Formula to find resistivity.

★ Formula to find area of circle.

★ Formula to convert diameter into radius

Using formula -

★ ${\sf{\rho = \: \: R \dfrac{A}{I}}}$

★ ${\sf{A = \: \: \pi r^{2}}}$

★ ${\sf{r = \: \: \dfrac{d}{2}}}$

Where -

★ ρ denotes resistivity

★ R denotes resistance

★ A denotes cross sectional area of wire.

★ I denotes Length of wire.

★ π is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r dentoes radius

★ ² denotes square

★ d denotes diameter

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Full solution -

~ Firstly let us convert the radius into diameter by using formula!

→ Radius = Diameter/2

→ Radius = 0.2/2

→ Radius = 0.1

~ Let's do this question firstly have to use formula to find area of circle then have to carry on according to the question!

→ Area = πr²

→ Area = 3.14(0.1)²

→ Area = 3.14 × 0.1 × 0.1

→ Area = 3.14 × 0.01

→ Area = 0.0314 mm²

∴ ρ = 10(0.0314/1000)

→ ρ = 0.000314Ω mm

→ ${\sf{\rho = \: \: 3.14 \times 10^{-7}}}$ Ω mm

• Henceforth, ${\sf{\rho = \: \: 3.14 \times 10^{-7}}}$ Ω mm is its resistivity.

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Answer 2

$\large{ \frak{ \red{Answer : }}}$

The resistivity of the conductor is $\bf 3.14\times10^{-7} \text{\O}$

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$\large{ \frak{ \red{Explanation:}}}$

$\sf⚕ \: { \purple{Let's \: understand \: the \: concept : }}$

⤏ This question says that the length of a wire is 1 metre and it is 0.2mm in diameter and has resistance of 10 ohms. We have to calculate it's resistivity.

${\frak{ \pmb{ \green{Given : - }}}}$

• Length(l) = 1 m
• Diameter(d) = 0.2 mm
• Radius(r) = 0.1 mm or 0.001 m
• Resistance(R) = 10 Ω

${ \frak{ \pmb{ \green{To \: Find :  -}}}}$

• The resistivity.

 $\large{ \frak{ \orange{Solution : }}}$

We know that,

${\bigstar{\boxed{\sf Area =\pi r^2}}}$

So,

⇒ 3.14 × 0.001 × 0.001

⇒ 0.00000314 m²

As we know,

${\bigstar{\boxed{\sf Resistivity = \dfrac{RA}{l}}}}$$\begin{gathered}\sf\\ \\\implies 10 \times \dfrac{0.00000314}{1}\\ \\ \\ \implies 0.0000314 \:Ω \\ \\ \implies 3.14\times10^{-7}\: Ω\end{gathered}$

Therefore, the resistivity of the conductor is $3.14\times10^{-7}\text{\O}mega m$.

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