Question

Calculate the resistance of 1 m long copper wire of radius 1 mm. Resistivity of the copper is 1.72 x 10-8 m
Pls answer this its urgent

Answer 1

Answer :-

Resistance of the wire is 0.0054 Ω .

Explanation :-

We have :-

→ Length of the wire (l) = 1 m

→ Radius (r) = 1 mm = 10⁻³ m

→ Resistivity (ρ) = 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 × 10⁻³⁻³

⇒ A = 3.14 × 10⁻⁶ m²

Now, let's calculate the resistance of the wire .

R = ρl/A

⇒ R = (1.72 × 10⁻⁸ × 1)/(3.14 × 10⁻⁶)

⇒ R = 1.72/3.14 × 10⁻⁸/10⁻⁶

⇒ R = 0.54 × 10⁻⁸⁺⁶

⇒ R = 0.54 × 10⁻²

⇒ R = 0.0054 Ω

Answer 2

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large\underline{\sf{\red{Given}}}$

✭ $\sf Length\: (l) \:of \:wire = 1\: m$

✭ $\sf Radius\: of \:wire = 1\: mm$

✭ $\sf Radius\: of \:wire\: in\: m = 10^{-3}\:m$

✭ $\sf Resistivity\: (\rho) = 1.72\:\times\:10^{-8}\:\Omega m$

$\large\underline{\sf{\blue{To\:Find}}}$

✭ $\sf Resistance\: of \:wire?$

$\large\underline{\sf{\green{Solution}}}$

Calculating area (A) of cross section of wire,

➝ $\sf A = \pi r^2$

➝ $\sf A = 3.14\:\times\:10^{-3}\:\times\:10^{-3}$

➝ $\sf A = 3.14\:\times\:10^{-3-3}$

➝ $\sf A = 3.14\:\times\:10^{-3-3}$

➝ $\sf \pink{A = 3.14\:\times\:10^{-6}\:m^2}$

Calculating resistance of wire,

➳ $\sf R = \dfrac{\rho\:\times\: l}{A}$

➳ $\sf R = \dfrac{1.72\:\times\:10^{-8}\:\times\:1}{3.14\:\times\:10^{-6}}$

➳ $\sf R = {\cancel{\dfrac{1.72}{3.14}}}\:\times\:10^{-8+6}$

➳ $\sf R = 0.54 \:\times\:10^{-2}$

➳ $\sf \pink{R = 0.0054\:\Omega}$

$\therefore\:{\sf{\underline{Resistance\:of\:wire = \bf{0.0054\:\Omega}}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━