Question

calculate the resistance of a copper wire 1 km long and 0.5 mm diameter. If the resistivity of copper is 1.7*10^-8 ohm meter...


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Answer 1

${ \huge {\underline {\underline {\mathtt {\blue{♡Answer}}}}}}$

$\mathbb{GIVEN :–}$

$\mathcal{• Length}\bf{(l) = 1 km = 1000m}$

$\mathcal{• Diameter} \bf{= 0.5mm =》 Radius = 0.25 mm}$

$\mathcal{• Resistivity = \bf 1.7 \times 10^{-8}1.7×10 </p><p>−8}$

$\mathbb{TO \: FIND :–}$

$\mathcal{• \: Resistance = ?}$

$\mathbb{SOLUTION :–}$

$\mathcal{• We \: know \: that –}$

$\begin{gathered} \\ \large\implies{ \boxed{\bf R = \dfrac{ \rho \: l}{A}}} \\ \end{gathered}$

$\mathcal{• Now Put The Values –}$

$\begin{gathered} \\\implies\bf R = \dfrac{1.7 \times {10}^{ - 8} \times 1000}{\pi {r}^{2} } \\ \end{gathered}$

$\begin{gathered} \\\implies\bf R = \dfrac{1.7 \times {10}^{ - 8} \times {10}^{3} }{\pi {r}^{2} } \\ \end{gathered} </p><p>$

$\begin{gathered} \\\implies\bf R = \dfrac{1.7 \times {10}^{ - 5}}{\pi {(0.25 \times {10}^{ - 3} )}^{2} } \\ \end{gathered}$

$\begin{gathered} \\\implies\bf R = \dfrac{1.7 \times {10}^{ - 5}}{3.14\times 0.0625 \times {10}^{ - 6}} \\ \end{gathered}$

$\begin{gathered} \\\implies\bf R = \dfrac{1.7 \times {10}^{ (- 5 + 6)}}{0.19625} \\ \end{gathered}$

$\begin{gathered} \\\implies\bf R = 8.662 \times 10^1 \\ \end{gathered}$

$\begin{gathered} \\\implies \large\pink{ \boxed{\bf R = 86.62 \: ohm}}\\ \end{gathered}$

Answer 2

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