Question

A steel trolley-car rail has a cross-sectional area of$\mathbf{56}\mathbf{.}\mathbf{0}{\mathbf{cm}}^{\mathbf{2}}$. What is the resistance of 10.0 kmof rail? The resistivity of the steel is$\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathbf{\Omega m}$.

Short answer

The resistance of 10km rail is $0.536\Omega$.

Step-by-step solution

The given data

a) Cross-sectional area,$A=56.0\times {10}^{-4}{m}^2$

b) Resistivity,$\rho =3.00\times {10}^{-7}\Omega .m$

c) The length of the rail,$L=10.0\times {10}^{3}m$

Understanding the concept of the resistance

If a steel trolley car rail moves with its speed having a particular cross-section area, we can find the resistance of that rail by considering the formula for resistance R= ρL/A, where, is the resistivity of the steel and L is the distance traveled by rail and A is its cross-sectional area.

Formulae:

The resistance value of a material, $R=\frac{\rho L}{A}$ (i)

Calculation of the resistance

Using the given data in equation (i), we can get the value of the resistance of the rail as follows:

$$\begin{gathered} R=\frac{\left(3.00\times {10}^7\right)\left(10\times {10}^3\right)}{\left(56.0\times {10}^{-4}\right)} \\ =0.536\Omega \end{gathered}$$

Hence, the value of the resistance is $0.536\Omega$.