Question

A steel trolly-car rail has a cross-sectional area of $56c{m^2}$. What is the resistance of $10.0km$ rail? The resistivity of the steel is $3.00 \times {10^{ - 7}}\Omega .m$.

Answer 1

To solve this question we should about the ohm’s law and basics about the resistance.
Resistance: In electric circuits, voltage is applied across electric circuits which cause current to flow in circuit and current flow feels opposition and the measure of the opposition to current flow is called resistance.
According to ohm’s law voltage is directly proportional to current and proportionality constant is called as resistance. The resistance depends upon the shape, size, and material.
Unit of resistance is ohm.
Formula used:
$R = \ell \dfrac{L}{A}\Omega$

Complete Step by step solution:
As, given in question,
The length of rail is $=$ $10k.m.$ $=$ $10000m$ .
Area of cross section $=$ $56c{m^2}$ = $0.0056{m^2}$ .
Resistivity of material $=$ $3.00 \times {10^{ - 7}}\Omega .m$ .
Substituting the values in the above formula,
$R = 3 \times {10^{ - 7}}\dfrac{{10000}}{{0.0056}}\Omega$
$R = 5.357\Omega$
Hence, resistance of given material will be $R = 5.357\Omega$ .

Additional information:
1. High resistance means the material is insulator and if resistance is low then material will be conductor.
2. Superconductors have resistance equal to zero.
3. Resistivity of material doesn't change with physical property but only change with change in atomic structure.
4. Ohms law can be used to determine voltage, resistance or current of an electric circuit and it is used to maintain the desired voltage drop across electric components.
5. Ohm's law is used in ammeter and dc shunts.

Note:
1. Should know about the unit conversion and check the given units before solving the question all variables should be in the same unit.
2. Must check resistivity is given in question or conductivity.
$\ell$ $=$ $\dfrac{1}{\sigma }$
3. Ohm law is not applicable for elements like diodes and transistors as they allow the current to flow through in one direction only.
4. Ohms law is not universal law because ohm's law is applicable to ohmic conductors but it cannot be used for non-ohmic conductors.