Question

The resistance of a wire of length $300m$ and cross-section area $1.0m{m}^2$ made of material of resistivity $1.0\times {10}^{-7}\Omega m$ is ___.

Answer 1

Step 1: Given Data

Resistance of the wire, $R$=?

Resistivity of the wire, $\rho =1.0\times {10}^{-7}\Omega m$

Length of the wire, $l=300m$

Area of the cross-section of wire, $A=1.0m{m}^2$

Step 2: Formula Used

The resistance $R$ is defined by $R=\frac{\rho l}{A}$, where $\rho$is the resistivity, $l$ is the length and $A$ is the area of the cross-section.

Step 3: Converting area of cross-section into standard units

We know that $1mm={10}^{-3}m$, so

$$\begin{gathered} A=1.0m{m}^2 \\ A=1.0\times {10}^{-6}{m}^2 \end{gathered}$$

Step 4: Calculation of the resistance of the wire

$$\begin{gathered} R=\frac{\rho l}{A} \\ R=\frac{1.0\times {10}^{-7}\times 300}{1.0\times {10}^{-6}} \\ R=300\times {10}^{-1} \\ R=30\Omega \end{gathered}$$

Thus, the resistance of a wire of length $300m$ and cross-section area $1.0m{m}^2$ made of material of resistivity $1.0\times {10}^{-7}\Omega m$ is $30\Omega$.