Question

Calculate the resistance of 1km long copper wire of radius 1 mm.

$( \tt{specific \: resistance \: of \: }\\ \tt{ \ copper \: is \: 1.72 × 10^-8 \: Ω m)}$
​

Answer 1

$\color{black}\boxed { \color{navy}{\mathbb{SOLUTION:}}}$

$\mathtt{ \star \: Given}$

$l = 1{km}$

We know that:

1 km = 1000m

$r = 1mm = 10 ^{ - 3} m$

$A = \pi {r}^{2}$

$= 3.14 \times (10 ^{ - 3})^{2}$

$= 3.14 \times 10 ^{6} \: m ^{2}$

$\rho = 1.72 \times 10 ^{ - 8} Ωm$

$\color{red}\boxed{ \color{navy}formula \: used : \color{black}R = \rho \frac{l}{A} }$

$= \frac{(1.72 \times {10}^{ - 8}) \times 1000 }{3.14 \times {10}^{ - 6} }$

$= 5.5 \: Ω$