Resistivity

Resistivity is the measurement of an object’s resistance. The resistivity of various materials differs since they have different resistance. Moreover, the resistivity of any object depends on several factors. Three classes are formed based on these factors, namely conductors, insulators, and semiconductors.  The conductors have low resistance, and insulators are the converse of them. On the other hand, the semiconductors are moderate conducting objects. Temperature, area, and length are factors that affect resistivity. 

The Resistivity of various materials

In a nutshell, resistivity is the general property of every element that either obstructs or enhances the electricity flow. Moreover, the higher the resistivity, the harder it gets for the current to flow—similarly, the low the resistivity, the smoothing the flow. The SI unit of Resistivity is ohm metre. And, a Greek letter ‘Rho’ (ρ) is used to depict resistivity in equations.

When discussing the resistivity of various materials, any component is regarded as a good or bad conductor of electricity based on its resistivity. The resistivity also categorises the elements in the classes of conductors, semiconductors, and insulators. For instance, here are the usual resistivity measures for categories. 

• Conductors: They have low resistivity as compared to other classes. Though electricity can flow easily, metals such as silver, copper, and gold are some examples.
• Semiconductors: These are materials that have moderate resistivity. Electricity flows through these conductors with few obstructions. Silicon and germanium are examples.
• Insulators: The materials which have high resistivity fall in this category. Paper and stone are some examples. 

Factors affecting Resistivity

• Area of cross-section: The electric resistivity of any element relies on the cross-section area. The primary dependence is on the type of cross-section area and how broad it is. For example, areas of conductors will allow the electricity flow more than that of insulators.
• Length of element: In a nutshell, suppose in an insulator, if the length would be more, the electricity will take more time since there is high resistance. On the other hand, even after obstructing the same opposition, the electricity will bypass through the material at the same speed. However, it will leave it quickly since the material is not broad enough.
• Temperature dependence of Resistivity- The element’s thermal energy increases its resistance in high temperatures. This results in a high electrical resistivity. Conversely, high temperatures cause the element’s resistance to decrease. Moreover, the class mainly determines the temperature dependence of resistivity. 

• Conductors: Conductors are a suitable element for electric conductivity because they have a minimal temperature dependence of resistivity, and the electricity travels at a quicker rate in certain elements.
• Semiconductors: These have a moderate temperature dependence of resistivity. 
• Insulators: They are highly dependent on the temperature. Though, they have high resistivity. 

Resistivity and examples

Let us look at some examples to understand resistivity better.

Example #1 

An element is placed between the ends of the circuit. The element’s resistance is 9 Ω, and the area of cross-section is 1500 cm2. And the length element is 30 cm. What will be the resistivity of the object?

Given, 

Resistance of element = 9 Ω

Length = 30 cm = 0.30 m

Area of cross section = 1500 cm2 = 0.15 m2,

• To find: Resistivity = Resistance * area / length

Therefore, Resistivity = 9 * 0.15 m2 / 0.30 m

= 1.35 Ω m2 / 0.30 m

= 4.5 Ω m

The above calculations show that the element has a resistivity of 4.5 Ω m(ohm metre). 

Example#2

The same element is placed with the same resistance and area in a circuit, just the length, and is doubled. Calculate the resistivity.

Given, 

Resistance of element = 9 Ω

Length = 30 cm * 2 = 0.60 m

Area of cross section = 1500 cm2 = 0.15 m2,

• To find: Resistivity = Resistance * area / length

Therefore, Resistivity = 9 * 0.15 m2 / 0.60 m

= 1.35 Ω m2 / 0.60 m

= 2.25 Ω m

Though, from both the above examples, we observed that as the length of the element doubled, the resistivity was halved. Why does this happen? The resistance was the same at both places, and in the second case, the resistance decreased since the length was more and the resistance scattered more than in the first case.

Conclusion

From all the above, we came through different aspects of resistivity. We concluded resistivity is the power that resists the electricity flow. Electrical resistivity is crucial since it enables the proper materials to be used in the proper positions in electronics. The resistance of superconductors, like those employed in electronics and ordinary connecting wires, must be below. Moreover, whether the element has high or low resistivity can be determined by classes, namely, conductors, insulators, and semiconductors.