Otis Singleton
Electrical resistance is a measure of how much an object opposes the flow of electric current. It is influenced by factors such as the material's composition, size, shape, and temperature. The SI unit of electrical resistance is the ohm, represented by the symbol Ω. As the length of a conductor increases and its cross-sectional area decreases, its resistance also increases. This relationship is described by Ohm's law, which states that resistance and voltage are directly proportional. The surface resistance of a material is influenced by the geometry and distance of the electrodes used to measure it. This article will explore the relationship between electrical resistance and surface area, considering various factors that influence this relationship.
| Characteristics | Values |
|---|---|
| Definition of electrical resistance | The measure of how much an object opposes the flow of electric current |
| SI unit | Ohm (Ω) |
| Factors that influence resistance | Material, size, shape, temperature, strain, light, humidity, contamination |
| Relationship between resistance and surface area | Resistance is inversely proportional to surface area |
| Relationship between resistance and conductivity | Resistance and conductivity are reciprocal quantities |
| Examples of materials with high resistance | Rubber, glass, distilled water |
| Examples of materials with low resistance | Metals (e.g. copper, aluminium), salt water |
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What You'll Learn
The relationship between resistance, resistivity, and conductivity
The electrical resistance of an object is influenced by its material composition and physical attributes, such as size and shape. These factors are quantified by the related concepts of resistivity and conductivity, which describe how strongly a material resists or conducts electric current.
Resistivity, also known as volume resistivity or specific electrical resistance, is a fundamental property of a material. It is denoted by the Greek letter rho (ρ) and measured in ohm-metres (Ω⋅m). Resistivity quantifies the inherent resistance of a material to electric current, with low resistivity indicating a material that readily conducts electricity. The resistivity of different materials can vary significantly; for example, the resistivity of Teflon is about 1030 times higher than that of copper. This variation is due to the different microscopic structures and electron configurations of materials. Metals, for instance, have a large number of "delocalized" electrons that are free to move across large distances, facilitating electrical conduction. In contrast, insulators like Teflon have electrons tightly bound to individual molecules, requiring a much greater force to displace them.
Conductivity, or specific conductance, is the reciprocal of resistivity. It represents a material's ability to conduct electric current and is commonly denoted by the Greek letter sigma (σ). The SI unit of electrical conductivity is Siemens per metre (S/m). Similar to resistivity, conductivity values can vary drastically between materials. For instance, metals like copper are considered highly conductive, while insulators like rubber have very low conductivity.
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The effect of surface area on resistance
The electrical resistance of an object is a measure of how much it opposes the flow of electric current. The SI unit of electrical resistance is the ohm, denoted by the symbol Ω. The reciprocal of resistance is electrical conductance, which measures how easily an electric current passes through an object.
The resistance of an object depends on the material it is made of, as well as its size and shape. For instance, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. This is because the cross-sectional area of the object affects its resistance. When a conductor is placed under tension, its length increases and its cross-sectional area decreases, leading to increased resistance. On the other hand, under compression, the cross-sectional area increases and the resistance decreases.
The surface resistance of an object is the ratio of DC voltage to the current flowing between two electrodes of a specified configuration that are in contact with the same side of the material. The unit of surface resistance is the ohm. The surface resistance depends on the geometry and distance of the electrodes used, and different types of electrodes would yield different results for the same specimen.
Therefore, it is clear that the surface area of an object does indeed affect its electrical resistance.
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How temperature impacts resistance
The electrical resistance of an object is a measure of how much it opposes the flow of electric current. It is influenced by factors such as the material's composition, size, shape, and temperature. While the surface area of an object does not directly determine its electrical resistance, changes in surface area can impact the resistance by altering the object's geometry. For instance, a wire's resistance is higher if it is long and thin, and lower if it is short and thick.
Now, let's delve into the relationship between temperature and resistance in more detail:
Temperature has a significant influence on the resistance of a material. In most cases, as the temperature rises, the resistance also increases. This relationship can be attributed to the increased thermal energy causing atoms in the material to vibrate more vigorously, impeding the flow of electrons and resulting in higher resistance. This phenomenon is particularly evident in metals. However, it's important to note that the temperature-resistance relationship can vary depending on the specific material and its intrinsic properties.
The impact of temperature on resistance is not linear. As temperature deviates from absolute zero, the resistance may exhibit complex behaviour. For instance, in semiconductors, as temperature increases from absolute zero, the resistance initially decreases steeply as carriers leave the donors or acceptors. However, once most of the carriers have departed, the resistance begins to increase slightly due to the reduced mobility of the remaining carriers.
The relationship between temperature and resistance is described by the Steinhart-Hart equation for semiconductors and the Wiedemann-Franz law for materials where heat and charge transport is dominated by electrons. These equations provide valuable tools for understanding and predicting the behaviour of resistance in response to changes in temperature.
Additionally, the effect of temperature on resistance is not limited to solids. In electrolytes, such as salt water, the electrical conduction is facilitated by the movement of ions. As the temperature of the electrolyte solution increases, the ions move more rapidly, leading to a decrease in resistance. This behaviour highlights that the temperature-resistance relationship can vary depending on the state of matter and the underlying conduction mechanism.
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The role of strain and tension on resistance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its value depends on the material it is made of, its size and shape, and other factors like temperature or strain.
The impact of strain and tension on resistance is not limited to the conductor's geometry changes. The material's intrinsic properties, such as its crystal structure, can also be affected. For example, in semiconductors, the doping level plays a crucial role in determining the temperature profile of resistance. At extremely low temperatures, some materials exhibit superconductivity, with zero resistance and infinite conductance. Additionally, the environmental conditions, such as temperature, humidity, and contamination, can influence the resistance, especially in the case of insulation resistance between adjacent conductors on a surface.
Furthermore, the concept of photoconductivity introduces another dimension to the role of strain and tension on resistance. Some resistors, particularly those made from semiconductors, exhibit photoconductivity, where their resistance changes when exposed to light. This behaviour highlights the interplay between strain, tension, and other external factors in influencing the overall resistance of a material.
In conclusion, the role of strain and tension on resistance is multifaceted. It involves changes in the geometry of the conductor, intrinsic material properties, environmental conditions, and interactions with external factors like light. Understanding these complexities is essential for designing and predicting the behaviour of electrical systems, especially in applications where precise control and measurement of resistance are critical.
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Superconductivity and zero resistance
Superconductivity is a set of physical properties observed in certain materials, known as superconductors, where electrical resistance vanishes and magnetic fields are expelled. This phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes.
The occurrence of superconductivity is dependent on temperature. Unlike ordinary metallic conductors, whose resistance decreases gradually as temperatures are lowered, a superconductor will only exhibit superconductivity below a critical temperature unique to the material. When the temperature is lowered enough, the resistance drops abruptly to zero.
The formation of Cooper pairs is integral to the occurrence of superconductivity. When the material is in a low-energy state (10-100 Kelvin), Cooper pairs form, and these have integer spins, meaning they form composite bosons. The lattice vibrational energy (phonons) are also bosons. The energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy that must be supplied to excite the fluid. If this energy is not supplied, the Cooper pair fluid becomes a superfluid, meaning it can flow without energy dissipation.
In the class of superconductors known as Type II superconductors, a very low but non-zero resistivity appears when an electric current is applied in conjunction with a strong magnetic field. This is due to the motion of magnetic vortices in the electronic superfluid, which causes some of the energy carried by the current to be dissipated. However, if the current is sufficiently small, the vortices are stationary, and the resistivity vanishes.
Superconductivity has many applications, such as in superconducting magnets, which can create very strong magnetic fields. These magnets are used in MRI machines and have been a focus of Toshiba's research since the early 1960s.
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Frequently asked questions
Yes, electrical resistance depends on surface area. The resistance of an object is influenced by its size and shape, with larger surface areas leading to increased resistance.
Electrical resistance is a measure of how much an object opposes the flow of electric current. It is quantified in ohms (Ω).
Conductance is the reciprocal of resistance, measuring how easily electric current passes through an object. Higher resistance results in lower conductance.
A longer conductor will have higher resistance compared to a shorter one, assuming the same material and cross-sectional area.
No, different materials have varying resistance properties. For example, electrical insulators like rubber tend to have high resistance, while conductors like metals have low resistance.
