91Ó°ÊÓ

In an electrical circuit, resistance is a measure of the resistance to current flow. The Greek letter omega$\left(\mathrm{Î\copyright }\right)$is used to represent resistance in ohms.

The electrical resistance of the value $R$of a resistive circuit element depends on its geometric structure (its length symbolized as $L$and cross-sectional area symbolized as $A$) and on the resistivity $\mathrm{ÒÏ}$of the material of which it is made:

$R=\mathrm{ÒÏ}\frac{L}{A}$

• The length of the wire is: $\mathrm{L}=20.0 \mathrm{m}$.
• The diameter of the wire is: $\mathrm{D}=2.053\mathrm{mm}×\frac{1\mathrm{m}}{1000\mathrm{mm}}=2.053×{10}^{-3}\mathrm{m}$.
• The radius of the wire is: $r=D/2=1.0256×{10}^{-3}\mathrm{m}$.
• The resistivity of the copper is:$\mathrm{ÒÏ}=1.72×{10}^{-8}\mathrm{Î\copyright }·\mathrm{m}$ .

The resistance of the copper wire is found from the above equation as:

$R=\mathrm{ÒÏ}\frac{L}{A}$

The value of $A=\mathrm{Ï€}{r}^2$, which is the cross-sectional area of the wire:

$R=\mathrm{ÒÏ}\frac{L}{\mathrm{Ï€}{r}^2}$

Entering the values, we obtain:

$$\begin{gathered} R=1.72×{10}^{-8}\mathrm{Î\copyright }·\mathrm{m}×\frac{20.0}{\mathrm{Ï€}{\left(1.0265×{10}^{-3}\mathrm{m}\right)}^2} \\ =0.1038\mathrm{Î\copyright } \\ =0.1038\mathrm{Î\copyright }×\frac{1000\mathrm{³¾Î\copyright }}{1\mathrm{Î\copyright }} \\ =103.8\mathrm{³¾Î\copyright } \end{gathered}$$

Therefore, the resistance of the copper wire is: $103.8\mathrm{³¾Î\copyright }$.