3.2 Resistance and conductance
3 min read•august 6, 2024
and are key concepts in understanding how electricity flows through materials. They're opposites: resistance opposes current flow, while conductance allows it. These properties help us design circuits and choose the right materials for electrical applications.
and are intrinsic material properties that determine resistance and conductance. Measured in -meters and siemens per meter, they help us compare different materials' electrical behavior. Understanding these concepts is crucial for working with electrical systems.
Electrical Properties
Resistance and Conductance
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- Resistance measures the opposition to the flow of electric current through a material
- Measured in ohms (Ω)
- Higher resistance indicates greater difficulty for current to pass through
- Conductance quantifies the ease with which electric current can flow through a material
- Measured in siemens (S)
- Higher conductance indicates easier passage of current
- Resistance and conductance are inversely related
- As resistance increases, conductance decreases and vice versa
- Mathematically expressed as: , where G is conductance and R is resistance
Resistivity and Conductivity
- Resistivity is an intrinsic property of a material that quantifies its resistance to electric current
- Measured in ohm-meters (Ω⋅m)
- Depends on the material's composition and structure
- Examples: copper (1.68 × 10⁻⁸ Ω⋅m), silicon (640 Ω⋅m), rubber (1 × 10¹³ Ω⋅m)
- Conductivity is the reciprocal of resistivity and measures a material's ability to conduct electric current
- Measured in siemens per meter (S/m)
- Higher conductivity indicates better electrical conductivity
- Mathematically expressed as: , where σ is conductivity and ρ is resistivity
Units of Measurement
Ohm and Siemens
- Ohm (Ω) is the SI unit for measuring electrical resistance
- Named after German physicist Georg Ohm
- Defined as the resistance between two points of a conductor when a constant potential difference of 1 volt produces a current of 1 ampere
- Siemens (S) is the SI unit for measuring electrical conductance
- Named after German inventor Ernst Werner von Siemens
- Equivalent to the reciprocal of an ohm (1 S = 1/Ω)
- Commonly used in electrical engineering and circuit analysis
Fundamental Concepts
Inverse Relationship between Resistance and Conductance
- Resistance and conductance are inversely proportional
- Doubling the resistance halves the conductance, and vice versa
- This relationship is crucial for understanding the behavior of electrical circuits
- Allows for the calculation of one quantity when the other is known
- The inverse relationship is expressed mathematically as: and
- R represents resistance in ohms (Ω)
- G represents conductance in siemens (S)
Material Properties Affecting Resistance and Conductivity
- The resistance and conductivity of a material depend on its intrinsic properties
- Atomic structure, electron mobility, and presence of impurities influence these properties
- Materials with high electron mobility (metals) generally have low resistivity and high conductivity
- Materials with low electron mobility (insulators) have high resistivity and low conductivity
- Temperature affects the resistance and conductivity of materials
- For most metals, resistance increases with increasing temperature due to increased atomic vibrations
- Semiconductors exhibit decreased resistivity with increasing temperature due to the excitation of electrons into the conduction band
- Cross-sectional area and length of a conductor influence its resistance
- Resistance is directly proportional to the length and inversely proportional to the cross-sectional area
- Mathematically expressed as: , where ρ is resistivity, l is length, and A is cross-sectional area
Key Terms to Review (13)
Conductance: Conductance is the measure of how easily electric current can flow through a material, defined as the reciprocal of resistance. It is an important concept in understanding electrical circuits, as higher conductance indicates a greater ability for current to pass through a conductor. Conductance plays a crucial role in various applications, including circuit design and analysis, where it helps determine how components interact within a system.
Conductivity: Conductivity is the ability of a material to conduct electric current, which is determined by the movement of charged particles within that material. The level of conductivity is inversely related to resistance; as conductivity increases, resistance decreases. Understanding conductivity is crucial when evaluating materials for electronic devices and determining how effectively they can transmit electrical signals.
Four-wire measurement: Four-wire measurement is a technique used to accurately measure the resistance of a component while eliminating the effects of lead and contact resistance. By using separate pairs of wires for supplying current and measuring voltage, this method provides a more precise measurement of low resistances, which is essential in applications requiring high accuracy.
Kirchhoff's Laws: Kirchhoff's Laws are fundamental principles in electrical engineering that describe the behavior of electrical circuits, focusing on current and voltage relationships. These laws include Kirchhoff's Current Law (KCL), which states that the total current entering a junction equals the total current leaving, and Kirchhoff's Voltage Law (KVL), which asserts that the sum of the electrical potential differences (voltages) around any closed loop in a circuit is zero. These principles are essential for analyzing complex circuits, connecting various electrical concepts.
Multimeter: A multimeter is a versatile measuring instrument used to measure voltage, current, and resistance in electrical circuits. This tool can be analog or digital and is essential for troubleshooting and testing electronic devices, providing critical information about the performance and condition of circuits. It bridges the understanding of resistance and conductance as well as the behavior of sinusoidal sources and phasors by offering quantitative measurements necessary for analysis and design.
Ohm: An ohm is the unit of measurement for electrical resistance in a circuit. It quantifies how much a material resists the flow of electric current, establishing a relationship between voltage, current, and resistance as expressed by Ohm's Law. Understanding ohms is crucial when looking at how different materials conduct electricity, how temperature impacts resistance, and how components interact in various circuit configurations.
Ohm's Law: Ohm's Law is a fundamental principle in electrical engineering that relates voltage, current, and resistance in a circuit, typically expressed as $$V = I imes R$$. This relationship helps in understanding how electrical circuits function and allows for the calculation of one of these values if the other two are known, which is crucial in analyzing electrical devices and systems.
Parallel circuit: A parallel circuit is a type of electrical circuit in which two or more components are connected across the same voltage source, providing multiple pathways for current to flow. This configuration allows the voltage across each component to remain constant, while the total current is the sum of the currents flowing through each path, influencing resistance, power distribution, and overall circuit behavior.
R = v/i: The equation $$r = \frac{v}{i}$$ defines resistance, where 'r' represents resistance in ohms (Ω), 'v' is the voltage across a conductor in volts (V), and 'i' is the current flowing through it in amperes (A). This relationship illustrates how resistance impedes the flow of electric current, helping to understand how electrical devices function and how they can be optimized. The formula forms a cornerstone of Ohm's Law, which describes the behavior of electrical circuits and is fundamental to analyzing electronic devices.
Resistance: Resistance is a measure of the opposition to the flow of electric current in a circuit, quantified in ohms (Ω). It plays a crucial role in controlling the amount of current that can pass through a conductor and affects how electrical devices operate. Understanding resistance is vital for analyzing circuits, ensuring safety, and optimizing device performance.
Resistivity: Resistivity is a fundamental property of materials that quantifies how strongly they resist the flow of electric current. It is defined as the resistance of a uniform material of unit length and unit cross-sectional area and is typically represented by the symbol $$\rho$$. The resistivity of a material is affected by its temperature, composition, and physical state, influencing its ability to conduct electricity in various applications.
Series Circuit: A series circuit is a type of electrical circuit in which components are connected end-to-end, providing a single path for current to flow. In this configuration, the same current flows through each component, and the total voltage across the circuit is the sum of the voltages across each component, making it crucial for understanding concepts like charge, current, voltage, and power, as well as resistance and conductance.
Superposition Theorem: The superposition theorem states that in a linear circuit with multiple independent sources, the total current or voltage at any point can be found by algebraically adding the individual effects of each source while all other independent sources are turned off. This principle is vital for analyzing complex circuits and simplifies calculations by breaking down the contributions from different sources, making it easier to understand the overall behavior of the circuit.