Physics Lesson 15.2.2 - Factors Affecting the Resistance of Materials

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Welcome to our Physics lesson on Factors Affecting the Resistance of Materials, this is the second lesson of our suite of physics lessons covering the topic of Electric Resistance. Combinations of Resistors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Factors Affecting the Resistance of Materials

Let's explain this point by considering the analogy between the electrons' flow through a conducting wire and a trip made by car. The road symbolically represents the conducting wire, and the drivers - including their cars - represent the moving electrons. Obviously, the physical state of a driver is highly affected by the trip conditions. If the trip is tedious, this is analogue to the resistance encountered by electrons during their flow through the conductor, i.e. more difficult the trip becomes for the driver, higher the resistance encountered by electrons during their flow through the circuit, based on the above analogy.

Let's consider the following scenarios:

1. If the trip is long, the car has to travel many kilometres. This takes a lot of time to the driver and as a result, he gets tired and loses concentration. There is an increased risk for accidents to occur if the driver doesn't stop to take a rest. This means longer the path, more difficult the trip becomes.
   Similarly, an electron flowing through a long wire has more probability to collide with other particles in the conductor than if the wire was shorter. This means the resistance of a conducting wire (R_w) increases with the increase in its length (L), i.e. resistance of wire is proportional to the length of conductor. We write
   
   R_w ~ L
2. If the road is new and well maintained, it is easier for the driver to travel along, but if the road is unpaved and full of holes etc., it becomes more difficult for the driver to travel on it. As a result, the trip takes more time and the driver gets tired faster.
   Similarly, the flow of electrons through a good conductor is easier than when they flow through a poorer conductor. This means a good conductor makes less resistance to electrons flow than a poorer conductor. This phenomenon is represented in formulae by a quantity known as resistivity, ρ, which shows how many ohms of resistance does a cube of 1 m side length makes to the flow of electrons through it (i.e. we put all materials in the same conditions to compare their conductive ability). Resistivity of a conductor (measured in Ω ∙ m) is an intrinsic property of material (i.e. it is given in tables, like density etc.) and is proportional to the resistance, i.e.
   
   R_w ~ ρ
3. If the road is wider (when the car in traveling on highways for example), the travel becomes easier than when the road is narrow. This is because the driver does not have to care about other cars; he can shift with his car through any lane he considers as more appropriate to avoid the traffic. Hence, the trip becomes easier when the road is wider.
   Similarly, electrons encounter less resistance when they flow through a wider cable than when they flow through a narrow wire. This means the resistance of a conducting wire is inversely proportional to its thickness (cross-sectional area, A). We write
   
   R_w ~ 1/A
   Combining all the three above factors in the same formula, we obtain for the resistance of conductor
   

Example 1

What is the resistance of a 20 m long and 6 mm² thick copper wire id the resistivity of copper is 1.69 × 10^-8 Ω ∙ m? Take the figure above as a reference.

Solution 2

First, we must convert the units into the standard ones. We have

L = 20 m = 2 × 10¹ m
A = 6 mm² = 6 × 10^-6 m²
ρ = 1.69 × 10^-8 Ω ∙ m
R_w = ?

Applying the equation for the resistance of conductor, we obtain

Remark! There is a fourth factor - the temperature of conductor - which affects the conducting ability of materials. As we have seen in the previous chapter, an increase in temperature brings an increase in the vibrational activity of material molecules around their equilibrium position. This brings an increase in the resistance of material as in such conditions it becomes more difficult for electrons to flow through the material without colliding. Imagine yourself walking through a hall in which people are running around. You have difficulty to walk, as besides carrying out the walking process you must take care to avoid collisions with other people. As a result, it takes you more time to reach the opposite wall. Therefore, we say temperature of material is proportional to the resistance. However, this factor is not represented in the above formula (it is intended only for cases in which the temperature of conductor is assumed as constant).

You have reached the end of Physics lesson 15.2.2 Factors Affecting the Resistance of Materials. There are 5 lessons in this physics tutorial covering Electric Resistance. Combinations of Resistors, you can access all the lessons from this tutorial below.

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