Question

Pls help this question

Answer 1

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$\huge{\underline{\sf{\red{Required\:Answer:}}}}$

• 122.72 m

$\large\underline\bold\green{Given:-}$

• Resistivity ρ = 1.6 × 10⁻⁸ Ω m

• Resistance R = 12 Ω

• Diameter d = 0.5 mm

$\large\underline\bold\red{To\:Prove}$

• The Length.

$\large\underline\bold\green{Solution:-}$

‣ Radius r = 0.25 mm = 0.25 × 10⁻³ m = 2.5 × 10⁻⁴ m

‣ Area A = 6.25 π × 10⁻⁸ m²

We are asked to find length L :

We know :

• $\large\boxed{\underline{\purple{\sf R = ρ \dfrac{L } {A }}}}$

• $\large\boxed{\underline{\orange{\sf L = \dfrac{R \times A }{ ρ } }}}$

Putting values here we get :

$\pink{\implies\:\:}$ L = ( 10 × 6.25 π × 10⁻⁸ ) / 1.6 × 10⁻⁸ m

$\pink{\implies\:\:}$ L = 62.5 π / 1.6

$\pink{\implies\:\:}$ L = 122.72 m.

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Answer 2

$\huge\underline\mathfrak\pink{Answer ♡}$

$\large\underline\bold\red{Given:-}$

diameter of copper wire = 0.5mm = 5 × 10-⁴ m

resistivity = 1.6 × 10^-8 ohm.m

resistance = 12 ohm

Length = ?

$\large\underline\bold\green{Formula\:used:-}$

$\dashrightarrow$ $\large{\underline{\blue{\sf L = \dfrac{R \times A }{ p } }}}$

where R , d , L and A are resistance , resistivity , length and cross section area.

$\large\underline\bold\red{Solution:-}$

$\implies$10 = 1.6 × 10^-8 × L/(πr²)

$\implies$L = 10 × 3.14 × (2.5 × 10^-4)² × 10^8/1.6

$\implies$L = 10× 3.14 × 6.25/1.6

$\implies$L = 122.656 m

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