Question

In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire.

Short answer

Resistance of wire$R=0.125\Omega$

Step-by-step solution

Step 1:

Given data:

$$\begin{gathered} d=2.05mm=2.05\times {10}^{-3}m \\ L=24.0m \end{gathered}$$

The cross-section of the area of the wire is:

$$\begin{gathered} A=\frac{\mathrm{\pi }}{4}{d}^2 \\ =\frac{\mathrm{\pi }}{4}\times {\left(2.05\times {10}^{-3}m\right)}^2 \\ =3.3\times {10}^{-6}{m}^2 \end{gathered}$$

As the copper resistivity is$\rho =1.72\times {10}^{-8}\Omega .m$

Putting the value of $\rho$, now the resistance is:

$$\begin{gathered} R=\frac{\rho L}{A} \\ =\frac{\left(1,72\times {10}^{-8}\Omega .m\right)\left(24.0m\right)}{3.3\times {10}^{-6}{m}^2} \\ =0.125\Omega \end{gathered}$$

Hence, the Resistance of a wire is$R=0.125\Omega$