Question

calculate the resistance of 1 km long copper wire of radius 1 mm. Resistivity of copper is =
$1.72 \times {10}^{ - 8} \: ohm$
​

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

calculate the resistance of 1 km long copper wire of radius 1 mm. Resistivity of copper is ${\sf 1.72×10^{-8}Ω.m}$

$\huge\underline{\underline{\bf \orange{Solution-}}}$

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

• Lenght of wire (L) = 1km = 1000m
• Radius (r) = 1mm = ${\sf 10^{-3}m}$
• Resistivity ${\sf (\rho)=1.72×10^{-8}ohm.m}$

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

• Resistance (R)

$\large{\rm We \: know \: that- }$

✪$\large{\boxed{\bf \blue{R=\rho\dfrac{L}{A}} }}$

$\implies{\sf R = 1.72×10^{-8}×\dfrac{1000}{πr^2} }$

$\implies{\sf R= 1.72×10^{-8}×\dfrac{1000}{3.14×(10^{-3})^2}}$

$\implies{\sf R = 1.72×10^{-8}×\dfrac{1000}{3.14×10^{-6}}}$

$\implies{\sf R = 1.72×10^{-8}×\dfrac{318.4}{10^{-6}} }$

$\implies{\sf R = 1.72×10^{-8}×318.4×10^6 }$

$\implies{\sf R = 547.6×10^{-2}}$

$\implies{\bf \red{ Resistance (R) = 5.4Ω }}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Resistance of copper wire is ${\bf \red{5.4Ω}}$.

Answer 2

Answer:

$\large\boxed{\sf{5.5 \;\;\Omega}}$

Explanation:

Given a copper wire :

Length, l = 1 km = ${10}^{3}\;m$

Radius, r = 1 mm = ${10}^{-3}\;m$

Resistivity, $\rho = 1.72 \times {10}^{-8}\; \Omega\:m$

To find the resistance, r :

find the Cross sectional area,

$= > a = \pi {r}^{2} \\ \\ = > a = \pi {( {10}^{ - 3} )}^{2} \\ \\ = > \sf{ a = {10}^{ - 6} \pi \: \: \: {m}^{2} }$

Now we know that,

$r = \rho \frac{l}{a} \\ \\ = > r = \frac{1.72 \times {10}^{ - 8} \times {10}^{3} }{ {10}^{ - 6} \pi} \\ \\ = > r = \frac{1.72}{3.14} \times {10}^{( - 8 + 3 + 6)} \\ \\ = > r = 0.55 \times {10}^{ 1} \\ \\ = > r = 5.5$

Hence resistance is $\bold{5.5 \;\;\Omega}$