Question

Calculate the resistance of a metal wire of length 2m and area of cross-section $1.55\times {10}^{-6}{m}^2$ , if the resistivity of the metal be $2.8\times {10}^{-8}$ Ωm?

Answer 1

Step 1: Given that:

Length($l$) of the metal wire= $\text{2m}$

Area of cross section($\text{A}$)= $1.55\times {10}^{-6}{m}^2$

Resistivity(ρ) of the metal= $2.8\times {10}^{-8}\text{Ω-}m$

Step 2: Calculation of resistance:

Resistance of a conductor is given by:

$R=\frac{\text{ρ}l}{A}$

Thus, putting all the values, we get

$R=\frac{2.8\times {10}^{-8}\text{Ω}-m\times 2m}{1.55\times {10}^{-6}{m}^2}$

$R=\frac{5.6\times {10}^{-2}}{1.55}$

$R=3.61\times {10}^{-2}\text{Ω}$

Thus,

The resistance of the metal wire is $3.61\times {10}^{-2}\text{Ω}$ .