Question

The length of copper wire is 100m and its radius is 1mm. Calculate the resistance if resistivity of copper is 1.72 x 10⁻⁸ Ωm.

Answer 1

$\boxed{\bold{Resistance=\frac{Resistivity\times Length}{Area}}}$

$\boxed{\bold{R=\frac{\rho\times l}{A}}}$

Here,

• $\rho = 1.72\times10^{-8}\:m$

• $l = 100\:m$

• $r = 1\:mm=0.001\:m$

• $A = \pi r^2=3.14\times (0.001)^2 = 3.14\times 10^{-6}\:m^2$

$\implies\bold{R=\frac{1.72\times10^{-8}\times 100}{3.14\times 10^{-6}}}$

$\boxed{\bold{\therefore{R=0.547\:\Omega}}}$

Answer 2

Answer:

$\bigstar{\bold{Resistance\:=\:0.55\:\Omega}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Length of wire (l) = 100 m
• Radius of wire (r) = 1 mm =0.001 m
• Resistivity (ρ) = 1.72 × 10⁻⁸Ω m

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Resistance (R)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ The area of the wire = πr²

   Area = 3.14 ×0.001 × 0.001 = 3.14 × 10⁻⁶ m²

→ The equation for finding resistance is given by

   $R\:=\:\dfrac{\rho\times l}{A}$

→ Substituting the given datas, we get

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

   $\boxed{\bold{Resistance\:=\:0.55\: \Omega}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Remember to convert all the given datas to the SI units before calculating.

→ Resistance is directly proportional to length of the conductor.

  $R\:\propto\:l$

→ Resistance is inversely proportional to area of cross section of conductor.

  $R\:\propto\:\dfrac{1}{A}$