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

GIVEN :–

• Length(l) = 1 km = 1000m

• Diameter = 0.5mm =》 Radius = 0.25 mm

• Resistivity = $\bf 1.7 \times 10^{-8}$

TO FIND :–

• Resistance = ?

SOLUTION :–

• We know that –

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

• Now put the values –

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

$\\\implies\bf R = \dfrac{1.7 \times {10}^{ - 8} \times {10}^{3} }{\pi {r}^{2} }$

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

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

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

$\\\implies\bf R = 8.662 \times 10^1$

$\\\implies \large{ \boxed{\bf R = 86.62 \: ohm}}$