Otis Singleton
Electrical resistance is a property of a circuit or circuit component that transforms electric energy into heat energy by opposing the flow of electric current. Every material has some electrical resistance, and it is denoted by the symbol 'R' and measured in ohms. The resistance of a conductor depends on its length, cross-sectional area, and the material it is made of. Resistivity, measured in ohm-meters, is a property of a material that quantifies its ability to oppose electric current. Conductors such as metals have low resistivity, while insulators like rubber have high resistivity.
| Characteristics | Values |
|---|---|
| Definition | Obstruction caused by a conductor to the flow of electric current |
| Formula | R = V/I |
| Unit | Ohm (Ω) |
| Factors Affecting Resistance | Length of the conductor, cross-sectional area, nature of the material, temperature |
| Zero Resistance | Superconductors |
| High Resistance | Open circuits, failed components, overheating components, voltage drop issues |
| Low Resistance | Short circuits |
| Fixed-Resistance Materials | Heating elements, resistors |
| Measurement Tools | Multimeter, ohmmeter |
| Resistivity | Measure of a material's ability to oppose electric current |
| High Conductivity and Low Resistivity Materials | Metals |
| Low Conductivity and High Resistivity Materials | Glass |
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What You'll Learn
Resistivity
The resistivity of a material is influenced by various factors, including temperature and purity. As the temperature of a metal increases, its resistance increases linearly. Conversely, as the temperature decreases, the resistivity follows a power law function of temperature. The Bloch–Grüneisen formula is used to approximate the mathematical relationship between temperature and resistivity. Additionally, the resistivity of a metal depends on its impurity concentration. When a metal is sufficiently pure and cooled to a very low temperature, its resistivity reaches a constant value known as the residual resistivity.
The geometry and size of a material also impact its resistivity. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. This relationship between resistance and geometry is described by Ohm's law, which states that the current through a material is proportional to the voltage applied across it. Materials that obey Ohm's law, such as wires and resistors, are called ohmic materials.
It is important to distinguish between resistivity and resistance. Resistivity is an intrinsic property of a material and represents its ability to oppose an electric current. On the other hand, resistance is an extensive property that depends on the specific object and its opposition to electric current. The resistance of an object is defined as the ratio of voltage across it to the current passing through it.
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Conductivity
The conductivity of a material depends on its physical nature and its physical shape and size, expressed by its length and sectional area. For instance, a wire's resistance is higher if it is long and thin, and lower if it is short and thick.
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Length and cross-sectional area
The electrical resistance of a conductor depends on several factors, including its length and cross-sectional area.
Firstly, electrical resistance is directly proportional to the length of the conductor. This means that as the length of a conductor increases, so does its electrical resistance. For example, a long wire will have higher resistance than a short wire of the same material and thickness.
Secondly, electrical resistance is inversely proportional to the cross-sectional area of the conductor. This means that as the cross-sectional area increases, the electrical resistance decreases. For instance, a thick wire will have lower resistance than a thin wire of the same material and length.
The relationship between length, cross-sectional area, and resistance can be observed in everyday objects. For example, a thick, short wire will have lower resistance than a thin, long wire made from the same material.
The length and cross-sectional area of a conductor are not the only factors that influence electrical resistance. The material of the conductor also plays a significant role, with different materials offering varying levels of resistance. Additionally, the temperature of the conductor can affect its resistance, with increasing temperatures generally leading to higher resistance.
It is also important to note that electrical resistance is distinct from resistivity, which is a property of the material used in the conductor. Resistivity measures the material's ability to oppose an electric current, while electrical resistance measures the obstruction to the current within a specific conductor.
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Temperature
At higher temperatures, the atoms in the conductor vibrate more vigorously, leading to increased collisions between free and captive electrons. These collisions impede the flow of electrons, resulting in greater resistance. This effect is particularly pronounced in conductive metals, where resistance typically increases with temperature.
However, it is important to note that different materials have varying temperature coefficients. Some metal alloys, for instance, exhibit very low positive temperature coefficients, resulting in minimal changes in resistance over a wide temperature range. This property is advantageous for the construction of precision resistors.
In contrast, insulators generally display a negative temperature coefficient, meaning their resistance decreases as temperature increases. This behaviour is attributed to the liberation of captive electrons due to the increased thermal energy. As more electrons become free to carry the current, the resistance decreases. Materials commonly used as insulators, such as glass and plastic, maintain their insulating properties over the typical temperature ranges they encounter.
The temperature dependence of resistance is also influenced by the geometry of the conductor and the material it is made from. For example, in some materials like silicon, the resistance decreases as temperature increases due to the unique behaviour of its atomic structure.
Engineers can exploit the temperature coefficients of different materials to create resistors with specific characteristics. By combining a resistor with a positive temperature coefficient and another with a negative temperature coefficient in series, it is possible to design a resistor with a resistance that remains relatively stable over temperature changes.
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Voltage and current
The electrical resistance of a conductor is the ratio of voltage across it to the current through it. Voltage, also known as electromotive force, is measured in volts. Current is measured in amperes, or amps. The unit of electrical resistance is ohms, represented by the Greek letter omega (Ω). One ohm is equal to one volt per ampere.
When a voltage source is connected to a conductor, it applies a potential difference that creates an electrical field. This electrical field then exerts a force on free charges, causing a current. The greater the resistance, the larger the field needed to produce a given current density.
The resistance of a conductor depends on its material, length, and cross-sectional area. For example, electrons flow more freely through copper than steel, and a long, thin wire has higher resistance than a short, thick wire. The nature of the material is quantified by its resistivity, or ability to oppose electric current. Resistivity is measured in ohm-meters (Ω⋅m). The higher the resistivity, the higher the resistance.
Ohm's law states that the current through a conductor is proportional to the voltage across it. Materials that follow Ohm's law are called ohmic materials, and include wires and resistors. The relationship between voltage and current can be visualised through a current-voltage graph, which for ohmic devices consists of a straight line through the origin with a positive slope.
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Frequently asked questions
Electrical resistance is the obstruction offered by a conductor to the flow of electric current. It is denoted by the letter 'R' and is measured in ohms.
The electrical resistance of a conductor depends on its length, cross-sectional area, and the material it is made of. For example, the resistance of a wire increases if it is long and thin and decreases if it is short and thick.
Resistivity is a property of a material that measures its electrical resistance or how strongly it resists electric current. It is denoted by the Greek letter rho (ρ). The SI unit of resistivity is the ohm-metre (Ω⋅m).
Superconductors are materials that have zero electrical resistance. They can carry an electric current indefinitely with no power source.
