Question

calculate the resistance of 1 kilometre long copper wire of radius 1 millimetre stability of copper 1.72 into 10 power minus 8 ohm metre​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

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

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Resistance (R)

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$\color{darkblue}\underline{\underline{\sf Formula \: Used-}}$

$\large\color{violet}\bullet\underline{\boxed{\sf R=\rho\dfrac{\ell}{A}}}$

A = Area = πr²

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$\implies{\sf R=1.7×10^{-8}×\dfrac{1000}{π×(10^{-3})^2} }$

$\implies{\sf R=1.7×10^{-8}×\dfrac{10^3}{3.14×10^{-6}}}$

$\implies{\sf R=1.7×10^{-8}\dfrac{10^{3+6}}{3.14}}$

$\implies{\sf R= \dfrac{17}{3.14}}$

$\color{red}\implies{\sf R=5.4\:Ω}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Resistance of copper wire is $\color{red}{\sf 5.4Ω}$

Answer 2

$\mathtt{\huge{ \fbox{Solution :)}}}$

Given ,

• Length of wire (l) = 1 km or 1000 m
• Radius of wire (r) = 1 mm or (10)^-3 m
• Resistivity (ρ) = 1.72 × (10)^-8 Ω m

We know that ,

$\large \mathtt{ \fbox{R = ρ \times \frac{length}{area} }}$

Thus ,

$\sf \hookrightarrow R = \frac{1.72 \times {(10)}^{-8} \times 1000 \times 7 }{22 \times {( {10}^{ - 3} )}^{2} } \\ \\ \sf \hookrightarrow R = \frac{172 \times {(10)}^{-5} \times 7}{22 \times {(10)}^{ - 4} } \\ \\ \sf \hookrightarrow R = \frac{1204 \times {(10)}^{-1} }{22} \\ \\ \sf \hookrightarrow R = 54.7 \times {(10)}^{-1} \\ \\ \sf \hookrightarrow R = 5.47 \: \: ohm$

Hence , the resistance of the wire is 5.47 ohm (Ω)

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