6.2 Resistance, resistivity, and Ohm's law
3 min read•august 7, 2024
, , and ###'s_Law_0### are key concepts in understanding how electric current flows through materials. These ideas help explain why some materials conduct electricity better than others and how voltage, current, and resistance are related.
Ohm's law, which states that voltage equals current times resistance, is a fundamental principle in electrical circuits. It allows us to predict how changes in voltage or resistance affect , making it crucial for designing and analyzing electrical systems.
Electrical Resistance
Resistance and Resistivity
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- Resistance quantifies the opposition to the flow of electric current in a material
- Measured in ohms (Ω) and represented by the symbol R
- Depends on the material's properties and dimensions ( and )
- Resistivity is an intrinsic property of a material that quantifies its resistance to current flow
- Measured in ohm-meters (Ω⋅m) and represented by the symbol ρ
- Relates to resistance through the equation , where L is the length and A is the cross-sectional area of the material
- Example materials with high resistivity: glass, rubber, and ceramics
- Example materials with low resistivity: metals like copper, silver, and aluminum
Conductivity and Temperature Coefficient of Resistivity
- Conductivity is the reciprocal of resistivity and measures a material's ability to conduct electric current
- Measured in per meter (S/m) and represented by the symbol σ
- Related to resistivity by
- of resistivity describes how a material's resistivity changes with temperature
- Represented by the symbol α and measured in units of per degree Celsius (°C⁻¹)
- For most metals, resistivity increases with increasing temperature, resulting in a positive temperature coefficient
- Example: copper has a temperature coefficient of resistivity of approximately 0.00393 °C⁻¹, meaning its resistivity increases by about 0.393% per degree Celsius increase in temperature
Ohm's Law
Ohm's Law and Its Applications
- Ohm's law states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it, with the constant of proportionality being the resistance (R)
- Mathematically expressed as [V = IR](https://www.fiveableKeyTerm:v_=_ir)
- Can be rearranged to solve for current () or resistance ()
- Applies to many materials, including most metals, over a wide range of voltages and currents
- Example: if a 10 Ω resistor has a voltage of 5 V across it, the current flowing through the resistor is
Series and Parallel Resistors
- Resistors can be connected in series or parallel to create more complex circuits
- Series resistors are connected end-to-end, and the total resistance is the sum of the individual resistances
- For n resistors in series:
- The current is the same through all resistors in series, while the voltage divides among them
- Parallel resistors are connected side-by-side, and the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances
- For n resistors in parallel:
- The voltage is the same across all resistors in parallel, while the current divides among them
Superconductivity
Superconductivity and Its Properties
- Superconductivity is a phenomenon in which certain materials exhibit zero electrical resistance and expel magnetic fields below a characteristic critical temperature
- Superconductors have a critical temperature (Tc) below which they transition to the superconducting state
- Example: mercury becomes a superconductor at temperatures below 4.2 K (-269°C)
- In the superconducting state, materials can carry electric current without dissipation, enabling efficient power transmission and high-field magnets
- Superconductors also exhibit the Meissner effect, where they expel magnetic fields from their interior, making them perfect diamagnets
- Applications of superconductivity include MRI machines, particle accelerators, and magnetic levitation (maglev) trains
Key Terms to Review (20)
Conductors: Conductors are materials that allow the flow of electric charge, primarily due to the presence of free-moving electrons. These materials, such as metals like copper and aluminum, have a high electrical conductivity, which means they can easily transmit electricity and heat. Conductors play a crucial role in the behavior of electric circuits and electromagnetic fields, influencing how resistance occurs and how electromagnetic induction can lead to phenomena like eddy currents.
Cross-sectional area: Cross-sectional area refers to the area of a cut surface or slice of an object, typically perpendicular to its length, which is crucial in understanding how that object conducts electricity. This term is directly connected to resistance and resistivity, as the size of the cross-sectional area affects the flow of electric current through a conductor. A larger cross-sectional area generally allows for more current to pass through, thereby reducing resistance and increasing conductivity.
Current flow: Current flow refers to the movement of electric charge, typically through a conductor like a wire, driven by an electric potential difference. This flow is essential in understanding how electrical circuits operate, as it determines how energy is transferred and consumed within devices. It is closely linked to resistance and resistivity, which describe how materials impede current flow, ultimately leading to Ohm's law that quantifies the relationship between voltage, current, and resistance.
Insulators: Insulators are materials that resist the flow of electric current and do not conduct electricity well. They play a crucial role in controlling electrical energy within circuits, preventing unwanted leakage of current and protecting components from short circuits. Their high resistivity makes them essential in electrical applications where safety and efficiency are priorities.
Length: Length is a measure of distance, typically defined as the extent of something from one end to another. In the context of resistance, resistivity, and Ohm's law, length is crucial because it directly influences the amount of resistance encountered by electric current as it flows through a conductor. The longer the conductor, the greater the resistance, which affects the overall performance of electrical circuits.
Material type: Material type refers to the classification of materials based on their electrical properties, which significantly influence resistance, resistivity, and Ohm's law. Different materials, such as conductors, insulators, and semiconductors, possess varying abilities to allow electric current to flow, affecting how they respond to applied voltage and current through Ohm's law. Understanding material types is crucial for predicting how different substances will behave in electrical circuits and applications.
Multimeter: A multimeter is a versatile electronic measuring instrument used to measure voltage, current, and resistance in electrical circuits. This tool is essential for diagnosing electrical issues and ensuring that components are functioning properly. By allowing users to conduct both DC and AC measurements, it plays a critical role in understanding and analyzing electrical properties and behaviors.
Ohm: An ohm is the unit of measurement for electrical resistance in a circuit, defined as the resistance between two points when a potential difference of one volt produces a current of one ampere. This unit connects to various concepts including how resistors behave in series and parallel configurations, the relationship between voltage, current, and resistance through Ohm's Law, and how to analyze complex circuits with multiple loops and resistances.
Ohm's Law: Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance of the conductor. This fundamental principle helps in understanding how voltage, current, and resistance interact within electrical circuits, linking concepts such as electric potential energy and current density with the behavior of resistors in series and parallel configurations.
Ohmmeter: An ohmmeter is an electrical device used to measure the resistance of a component or circuit in ohms. It helps in diagnosing issues within electrical systems by determining how much opposition there is to the flow of electric current. Understanding how an ohmmeter functions is essential for grasping the concepts of resistance, resistivity, and Ohm's law, as it provides practical insights into how materials conduct electricity and how resistance can impact circuit performance.
Parallel circuits: Parallel circuits are electrical circuits where multiple components are connected across the same voltage source, allowing current to flow through multiple paths. This configuration leads to shared voltage across components, but the total current is divided among them, which impacts resistance and overall circuit behavior. Understanding parallel circuits is essential for analyzing how resistors behave and how they follow Ohm's law in different configurations.
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 determining how much current will flow for a given voltage according to Ohm's law, and it influences the performance of electrical components and circuits, particularly in terms of energy dissipation as heat.
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 material per unit length and cross-sectional area, typically expressed in ohm-meters (Ω·m). The resistivity of a material is influenced by its temperature and composition, playing a critical role in determining how electrical current flows through different substances, impacting resistance and Ohm's law.
Semiconductors: Semiconductors are materials that have electrical conductivity between that of conductors and insulators, typically used in electronic devices. They can be manipulated to control the flow of electrical current, which is crucial for the operation of modern electronics such as diodes, transistors, and integrated circuits. The unique properties of semiconductors allow them to exhibit behaviors like rectification and amplification, which directly relate to electric current, current density, resistance, and Ohm's law.
Series circuits: A series circuit is an electrical circuit where components are connected end-to-end, forming a single path for current flow. In this configuration, the same current flows through each component, and the total resistance is the sum of the individual resistances. This setup affects voltage distribution across the components and can influence the overall performance of the circuit.
Siemens: Siemens is the SI unit of electrical conductance, symbolized as 'S', representing the ability of a material to conduct an electric current. It is defined as the reciprocal of resistance measured in ohms, meaning that a conductor with a conductance of one siemens has a resistance of one ohm. This unit connects to important concepts such as resistance and Ohm's law, which describe how current, voltage, and resistance are interrelated in electrical circuits.
Temperature Coefficient: The temperature coefficient is a numerical value that indicates how the resistance of a material changes with temperature. It is commonly expressed in terms of ohms per degree Celsius (Ω/°C) and helps to describe how conductors, insulators, and semiconductors behave when subjected to temperature variations. Understanding the temperature coefficient is essential for predicting how electrical components will perform under different thermal conditions, particularly in the context of resistance, resistivity, and Ohm's law.
Thermal resistance: Thermal resistance is a measure of a material's ability to resist the flow of heat. It quantifies how well an object can insulate against thermal energy transfer, indicating the effectiveness of materials in preventing heat conduction. This concept connects closely with resistance and resistivity, as it highlights how different materials can impede heat flow, just as electrical resistance affects the flow of current.
V = ir: The equation v = ir, known as Ohm's Law, describes the relationship between voltage (v), current (i), and resistance (r) in an electrical circuit. This fundamental principle illustrates how the voltage across a conductor is directly proportional to the current flowing through it, with the resistance acting as the proportionality constant. Understanding this relationship is crucial for analyzing circuits and understanding how electrical components behave under different conditions.
Voltage drop: Voltage drop refers to the reduction in voltage across a component or conductor in an electrical circuit, caused by the resistance of the material through which the current is flowing. This concept is crucial for understanding how electrical energy is distributed and consumed in various circuit configurations, affecting the overall efficiency and functionality of electrical systems.