Question

Find the length of a conductor having resistance 2 ohms , resistivity 1.6 × 10^-8 ohms and radius 1× 10^-3 m. pls tell me I will mark you in brainlist​

Answer 1

Answer :-

Length of the conductor is 392.5 m .

Explanation :-

We have :-

→ Resistance = 2 Ω

→ Resistivity = 1.6 × 10⁻⁸ Ωm

→ Radius = 1 × 10⁻³ m

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

= πr²

= 3.14 × 10⁻³ × 10⁻³

= 3.14 × 10⁻⁶ m²

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Now, we know that :-

R = ρL/A

Substituting values, we get :-

⇒ 2 = [1.6 × 10⁻⁸ × L]/3.14 × 10⁻⁶

⇒ 2 × 3.14 × 10⁻⁶ = 1.6 × 10⁻⁸ × L

⇒ 6.28 × 10⁻⁶ = 1.6 × 10⁻⁸ × L

⇒ L = [6.28 × 10⁻⁶]/[1.6 × 10⁻⁸]

⇒ L = 3.925 × 100

⇒ L = 392.5 m

Answer 2

Answer:

Given :-

• A resistance of 2 ohms, resistivity of 1.6 × 10-⁸ ohms and radius of 1 × 10-³ m.

To Find :-

• What is the length of a conductor.

Formula Used :-

$\clubsuit$ Area of Cross-section Formula :

$\longmapsto \sf\boxed{\bold{\pink{Area\: of\: Cross-section\: =\: {\pi}r^2}}}$

where,

• r = Radius

$\clubsuit$ Resistance Formula :

$\longmapsto \sf \boxed{\bold{\pink{R =\: \dfrac{\rho L}{A}}}}$

where,

• R = Resistance
• ρ = Resistivity
• L = Length
• A = Cross-sectional area

Solution :-

First, we have to find the area of cross-section :

Given :

• Radius = 1 × 10-³ m
• π = 22/7 × 3.14

According to the question by using the formula we get,

$\implies \sf Area\: of\: Cross-sectional =\: 3.14 \times {(1 \times 10^{-3})}^{2}$

$\implies \sf Area\: of\: Cross-sectional =\: 3.14 \times 1 \times 10^{-3} \times 1 \times 10^{-3}$

$\implies \sf Area\: of\: Cross-sectional =\: 3.14 \times 10^{-3} \times 10^{- 3}$

$\implies \sf Area\: of\: Cross-sectional =\: 3.14 \times 10^{(- 3 + - 3)}$

$\implies \sf Area\: of\: Cross-sectional =\: 3.14 \times 10^{(- 3 - 3)}$

$\implies \sf \bold{\green{Area\: of\: Cross-sectional =\: 3.14 \times 10^{-6}\: m^2}}$

Now, we have to find the length of a conductor :

Given :

• Resistance = 2 ohm
• Resistivity = 1.6 × 10-⁸ ohm m
• Cross-section area = 3.14 × 10-⁶ m²

According to the question by using the formula we get,

$\dashrightarrow \sf 2 =\: \dfrac{1.6 \times 10^{-8} \times L}{3.14 \times 10^{-6}}$

By doing cross multiplication we get,

$\dashrightarrow \sf 1.6 \times 10^{-8} \times L =\: 3.14 \times 10^{-6} × 2$

$\dashrightarrow \sf 1.6 \times 10^{-8} \times L =\: 6.28 \times 10^{-6}$

$\dashrightarrow \sf L =\: \dfrac{\cancel{6.28} \times 10^{-6}}{\cancel{1.6} \times 10^{-8}}$

$\dashrightarrow \sf L =\: 3.925 \times 10{^2}$

$\dashrightarrow \sf L =\: 3.925 \times 100$

$\dashrightarrow \sf L =\: \dfrac{3925}{1000} \times 100$

$\dashrightarrow \sf L =\: \dfrac{3925 \times 100}{1000}$

$\dashrightarrow \sf L =\: \dfrac{3925\cancel{00}}{10\cancel{00}}$

$\dashrightarrow \sf L =\: \dfrac{3925}{10}$

$\dashrightarrow \sf\bold{\red{L =\: 392.5\: m}}$

$\therefore$ The length of a conductor is 392.5 m .