Wiktor Wise
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. It is influenced by the material's temperature and composition, as well as its size and shape. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. Conductors, such as metals, have high conductivity and low resistivity, while insulators like rubber or plastic have low conductivity and high resistivity. The resistivity of a material is inversely proportional to its conductivity, and substances in which electricity can flow are called conductors. Silver is the most conductive element, followed by copper and gold, although copper is the most commonly used in electrical applications due to its affordability and corrosion resistance.
| Characteristics | Values |
|---|---|
| Definition | Resistivity is a measure of a material's ability to oppose an electric current. |
| Formula | \(\rho = \frac{1}{\sigma}\) |
| SI Unit | Ohm-meter |
| Relation to Conductivity | Conductors have high conductivity and low resistivity. Insulators have low conductivity and high resistivity. |
| Relation to Temperature | The electrical resistivity of a conductor decreases as the temperature is lowered. |
| Relation to Length | The resistance of a conductor is proportional to its length. |
| Relation to Cross-Sectional Area | The resistance of a conductor is inversely proportional to its cross-sectional area. |
| Relation to Material | The resistance of a conductor depends on the material it is made of. Metals tend to have low resistance, while insulators like rubber have high resistance. |
| Superconductors | Superconductors have zero resistance and infinite conductance. |
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What You'll Learn
Resistivity and conductivity
Resistivity is a measure of a material's ability to oppose electric current. It is the opposite of electrical conductivity, which is a measure of how easily a material can transmit electric current. The SI unit of electrical resistivity is the ohm-meter, denoted by the Greek letter Omega, Ω.
Materials with high conductivity, such as metals, have low resistivity, whereas materials with low conductivity, such as rubber, have high resistivity. Silver is the most conductive element, followed by copper and gold. However, copper and gold are more commonly used in electrical applications due to their cost-effectiveness and superior corrosion resistance, respectively.
The resistance of a conductor is influenced by several factors, including its length, cross-sectional area, temperature, and the material it is made of. For instance, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. Additionally, the resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
The electrical resistivity of a metallic conductor decreases as the temperature is lowered. In contrast, the resistivity of semiconductors decreases with increasing temperature. Superconductors are a special class of materials that exhibit zero resistance when cooled below their critical temperature, allowing an electric current to flow indefinitely without a power source.
The choice of materials for conductors depends on various factors such as cost, weight, reactivity, and physical strength. For example, while calcium and alkali metals have the best resistivity-density products, they are rarely used due to their high reactivity with water and oxygen and their lack of physical strength.
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Resistors and semiconductors
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. It is the inverse of electrical conductivity, where a material with high conductivity has low resistivity.
Resistors are a passive two-terminal electrical component that implements electrical resistance as a circuit element. They are used to reduce current flow, adjust signal levels, divide voltages, and bias active elements, among other uses. Resistors are composed of various compounds and forms, and their electrical function is specified by their resistance. The resistance of a conductor is influenced by its length, cross-sectional area, temperature, and the material from which it is made. For example, the resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
Resistors can be fixed or variable. Fixed resistors have resistances that only change slightly with temperature, time, or operating voltage, while variable resistors can be used to adjust circuit elements, such as volume control or a lamp dimmer. Resistors are rated according to their maximum power dissipation, with power resistors being physically larger and used in power supplies, power conversion circuits, and power amplifiers.
Semiconductors, on the other hand, are active components that display variable resistance. They can amplify the current flowing through them and their resistance can be dramatically changed by applying a sufficient forward bias voltage. The conductivity of a semiconductor is generally intermediate but can vary widely under different conditions, such as exposure to electric fields, specific frequencies of light, temperature, and composition.
While resistors and semiconductors both involve resistance, they are not the same. The function of a fixed resistor is to provide a fixed resistance, while a semiconductor component like a diode can switch between high and low resistance depending on the applied voltage.
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Length, area, and resistance
The electrical resistance between two points depends on several factors, including the conductor's length, cross-sectional area, temperature, and the material from which it is made.
The resistance of a conductor is directly proportional to its length. In other words, the longer the conductor, the greater the resistance. For example, if we take two identical conductors and connect them end-to-end, we double the total length, resulting in double the resistance. To achieve the same current, we would need to double the applied voltage.
Conversely, the resistance of a conductor is inversely proportional to its cross-sectional area. A larger cross-sectional area results in lower resistance. By doubling the cross-sectional area, we halve the resistance, and the required voltage is also halved to maintain the same current.
The material used also plays a significant role in determining the resistance. Conductors, such as wires and cables, generally have very low resistance values, while insulators, like plastic or air, exhibit high resistance. The resistivity of the material, which is a characteristic of the material itself, determines how much it resists the flow of charges.
Additionally, temperature influences resistance. In conductors, as temperature increases, so does resistivity because atoms vibrate more rapidly, causing more collisions with electrons. On the other hand, in semiconductors, resistivity decreases with increasing temperature due to increased thermal agitation, resulting in a higher number of free charges available to carry current.
The relationship between resistance, length, cross-sectional area, and resistivity can be observed in the formula for resistance, R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.
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Voltage, current, and resistance
Voltage
Voltage is the difference in charge between two points. It is a specific measure of potential energy that is always relative between two points. When we speak of voltage in a circuit, we are referring to the measurement of how much potential energy exists to move charge carriers from one particular point in that circuit to another particular point. It is measured in volts, which is the potential energy difference between two points that will impart one joule of energy per coulomb of charge that passes through it.
Current
Current is the rate at which the charge is flowing. It is the continuous movement of electric charge through the conductors of a circuit. The force motivating charge carriers to "flow" in a circuit is called voltage. The current in a wire is proportional to the voltage across it but inversely proportional to resistance.
Resistance
Resistance is a material's tendency to resist the flow of charge (current). It is the measure of the opposition to the current in a circuit. The amount of current in a circuit depends on the amount of voltage and the amount of resistance in the circuit to oppose current flow. The longer the conductor, the higher the resistance, and the greater the cross-sectional area of the conductor, the lower the resistance.
The relationship between voltage, current, and resistance is given by Ohm's Law, which states that the current in a wire is proportional to the voltage across it but inversely proportional to resistance. The formula for resistance, voltage, and current is expressed as I = V/R, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms.
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Superconductors and insulators
Electrical resistivity is the measure of how strongly a material opposes the flow of electric current. It is the reciprocal of electrical conductivity. Resistivity is influenced by factors such as the material's length, cross-sectional area, temperature, and composition. Conductors, such as metals, possess low resistivity, whereas insulators like glass exhibit high resistivity.
Superconductors are a unique class of materials that conduct electricity with zero resistance below a critical temperature unique to each material. This critical temperature is the point at which the resistance abruptly drops to zero, and it is usually very low, around -250 degrees Celsius. Superconductors are used in various applications, including Josephson junctions, which are the foundation of highly sensitive magnetometers called SQUIDs (superconducting quantum interference devices). They also find utility in photon detection and ultrasensitive bolometers.
The phenomenon of superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was investigating the resistance of solid mercury at extremely low temperatures. In a superconductor, the current is not driven by a voltage gradient but is instead related to the phase gradient of the superconducting order parameter. This results in the persistent flow of electric current in a loop of superconducting wire, even without a power source.
Superconductors can be classified as Type I or Type II. Type I superconductors have a single critical field, above which superconductivity is lost, while Type II superconductors allow partial magnetic field penetration through vortices.
Superinsulators, on the other hand, are materials that exhibit infinite resistance at low but finite temperatures, preventing the flow of electric current. The superinsulating state is sensitive to temperature increases and the application of external magnetic fields and voltage. The concept of superinsulation is closely related to superconductivity, with both phenomena relying on the pairing of conduction electrons into Cooper pairs. While superconductors enable coherent movement of these pairs, superinsulators confine both the Cooper pairs and normal excitations, preventing current flow.
The potential applications of superinsulators include their use in combination with superconductors to create switching electrical circuits with zero energy loss as heat.
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Frequently asked questions
Electrical resistivity is a measure of a material's ability to oppose an electric current. The higher the resistivity, the more the material resists the flow of electric current.
Conductors have high conductivity and low resistivity, whereas insulators have low conductivity and high resistivity. Metals, for example, are good conductors, while rubber is a common insulator.
The electrical resistivity of a conductor decreases as the temperature lowers.
Silver, copper, and gold are good electrical conductors. Silver is the most conductive element, but copper and gold are more commonly used due to their cost-effectiveness and superior corrosion resistance.
The resistivity of a conductor depends on its length, cross-sectional area, temperature, and the material it is made of.
