Physics, asked by harsh171087, 10 months ago

  Calculate the resistance of 2 km long copper wire of radius 2 mm. (Resistivity of copper = 1.72 x 1 0-8)​

Answers

Answered by Anonymous
11

\sf{\bf{Given}}\begin {cases} \sf{ The \:Length \:of\:copper\:wire\:is\:2\:km}& \\\\ \sf{ Radius \:of\:Copper\:wire\:is\:2\:mm}&\\\\ \sf{Resistivity \:of\:Copper \:is\:1.72\times 10^{8}}\end{cases}\\\\

Need To Find : The Resistance.

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⠀⠀⠀⠀⠀⠀⠀⠀❍ Converting Units : ⠀⠀

\sf{\bf{Converting\:units}}\begin {cases} \sf{ The \:Length \:of\:copper\:wire\:is\:2\:km\:or\:2000\:m\:or\:2 \times 10^{3} \:m.}& \\\\ \sf{ Radius \:of\:Copper\:wire\:is\:2\:mm\:or\:2 \times 10^{-3}}&\\\\ \sf{Resistivity \:of\:Copper \:is\:1.72\times 10^{8}}\end{cases}\\\\

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⠀⠀⠀⠀⠀⠀⠀⠀\underline{\frak{As\:We\:know\:that\::}}\\

⠀⠀⠀⠀⠀⠀⠀⠀⠀\pink{\boxed { \sf{Resistance = \dfrac{ Resistivity \:of\:Copper\:wire\: \times Length}{Area}}}}\\

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⠀⠀⠀⠀⠀⠀\underline {\sf{\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}}\\

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⠀⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ Resistivity \:of\:Copper\:wire\: \times Length}{Area}}}\\

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As , We know that :

Area of Wire = \pi\:\times Radius^{2}

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⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ Resistivity \:of\:Copper\:wire\: \times Length}{\pi\times Radius^{2}}}}\\

⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ 1.72 \times10^{-8}\times  2 \times 10^{3} \: }{\pi\times \big(2 \times 10^{-3}\big)^{2}}}}\\

⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ 1.72 \times10^{-8}\times  2 \times 10^{3} \: }{3.14 \times 4 \times 10^{-6}}}}\\

⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ 1.72 \times10^{-8}\times  2 \times 10^{3} \: }{12.56 \times 10^{-6}}}}\\

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☆ Now By Using Law's of Exponents :

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⠀⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ 1.72 \times \cancel {10^{-8}} \times  2 \times \cancel {10^{3}} \: }{12.56 \times \cancel {10^{-6}}}}}\\

⠀⠀⠀⠀⠀⠀⠀⠀[ 10 ^{(-8 + 3 + 6)} = 10 ^{-5 + 6}= 10 ^{-1} = 1 ]

⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ 1.72  \times  2  \: }{12.56 } }}\\

⠀⠀⠀⠀⠀⠀⠀:\implies { \sf{Resistance = \dfrac{ \cancel {34.4}\: }{\cancel {12.56} } }}\\

⠀⠀⠀⠀⠀⠀⠀:\pink{\boxed { \sf{Resistance =  2.7388 \:ohm}}}\\

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Therefore,

⠀⠀⠀⠀⠀\underline {\therefore\:{\pink{ \mathrm {The\:Resistance\:of\: Copper\:wire\:is\: =  2.7388 \:ohm  }}}}\\

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