Question

Calculate the resistance of a 100 m long wire having a uniform cross-section area of 0.02 mm^2 and having a resistivity of 0.04 miliohm-cm.

Answer 1

Answer:

Resistance of the wire is 2000 Ω.

Explanation:

Given:

$\sf{\rho = 0.04 \; m \Omega \; cm = 0.04 \times 10^{-5} \Omega \; m = 4 \times 10^{-7} \Omega \; m }$

$\sf{l = 100 \; m}$

$\sf{A = 0.02 \; mm^{2} = 0.02 \times 10^{-6} \; m^{2} = 2 \times 10^{-8} \; m^{2} }$

To find:

Resistance of the wire

Solution:

As we know,

$\sf{R = \rho \; \dfrac{l}{A} }$

Substituting the values,

$\hookrightarrow \sf{R = 4 \times 10^{-7} \times \dfrac{100}{2 \times 10^{-8}}}$

$\hookrightarrow \sf{R = \; \not 4 ^{^{^{\big 2}}} \times 10\not ^{-7} \times \dfrac{100}{\not 2 \times 10\not^{-8} \: _{_{{\big {10^{-1}}}}}}$

$\hookrightarrow \sf{R = 2 \times \dfrac{100}{10^{-1}}}$

$\hookrightarrow \sf{R = 2 \times 100 \times 10}$

$\hookrightarrow \sf{R = 2000 \; \Omega}$

Hence,

Resistance of the wire = 2000 Ω

Here,

ρ = resistivity

l = length of the wire

A = area of cross section

R = resistance