Electrical resistivity and conductivity
Electrical resistivity and conductivity are key concepts that describe how materials conduct electricity. They are inversely related; materials with high resistivity exhibit low conductivity and are poor conductors, often referred to as insulators, whereas those with low resistivity demonstrate high conductivity and are excellent conductors. The behavior of electrical charge in materials is rooted in the movement of electrons, which can transfer energy efficiently in conductive materials like metals, such as copper and silver. In contrast, insulators like wood and rubber resist the flow of electric charge.
Resistance, a measure of opposition to electric current, depends on current, voltage difference, and the properties of the material, with resistivity being a critical factor influenced by material composition, size, and temperature. For instance, while metals generally have low resistivity, materials like glass have high resistivity, making them poor conductors. Conductivity, the reciprocal of resistivity, also helps quantify how well a material can conduct electricity, with units measured in mhos per meter. Understanding these principles is essential for applications in electronics, energy distribution, and various technological fields.
Electrical resistivity and conductivity
Both electrical resistivity and electrical conductivity relate to how well materials are able to conduct electricity. Resistivity and conductivity have a reciprocal, or inverse, relationship. Materials with high resistivity and low conductivity are poor conductors, or insulators. Materials with low resistivity and high conductivity are excellent conductors. To understand resistivity and conductivity, an understanding of fundamental principles of electrons and electricity is essential.
Electrons and Electricity
An atom is the smallest unit of matter that can exist by itself. Very small particles of matter, called subatomic particles, make up atoms. Subatomic particles include protons, neutrons, and electrons. Protons have a positive electrical charge. Neutrons are neutral, which means they have no electrical charge. Electrons have a negative electrical charge.
Atoms contain an equal number of protons and electrons. The equal but opposite charges of protons and electrons balance each other, creating an atom with no net electrical charge, or a neutral atom. Protons and neutrons are confined within the nucleus, or the central part of an atom. Electrons, however, orbit the nucleus at a distance and have much more freedom of movement than protons do. Electricity is a form of energy that occurs as a result of the movement of electrons.
Some atoms and molecules (groups of atoms) readily give up electrons while others keep a firm grip on them. Objects become charged when electrons move from one location to another. The Law of Conservation of Charge states that charge cannot be created or destroyed but can be transferred from one object to another. For example, as a person walks across a carpet, the carpet molecules readily give up electrons, which build up on the person's skin. As a result, the person's skin, having gained electrons, becomes negatively charged; the carpet, having lost electrons, becomes positively charged.
Materials that contain many free electrons allow for the movement of electrons and the free flow of electric charge, also known as electric current. These materials are conductors. Examples of good conductors are metals such as silver, gold, and copper. Electrical wires that deliver electricity to homes and businesses often contain copper wire because copper is such a good conductor of electricity.
Materials composed of atoms and molecules that hold tightly to their electrons are called insulators. Insulators resist the movement of electrons and the flow of electric charge. Insulators, therefore, are poor conductors of electricity. Examples of good insulators are wood, rubber, and plastic. Cords for products such as toasters and coffee makers have a layer of insulating plastic wrapped around their wires to protect against electric shock.
Resistivity
Resistance is opposition to the flow of an electric current. As electrons move through a conductor, they bump into the atoms that make up the conducting material. These impacts cause resistance. They also convert some electrical energy into thermal energy, or heat.
Resistance depends on two factors: current and voltage difference, also known as potential difference. The voltage difference is the amount of work it takes to transfer a charge from one place to another. Resistance is measured in units called ohms (Ω), current is measured in units called amperes (A), and voltage difference is measured in units called volts (V). The following formula can be used to determine resistance:
, where R represents resistance, V represents voltage (potential) difference, and I represents current. As a whole, the resistance formula establishes the relationship among resistance, voltage difference, and current.One other factor that influences a conductor's resistance is resistivity. Resistivity is measured in units called ohm-meters (Ω-m). Resistivity depends on the material composition, length, and thickness of the conductor. For example, silver, a metal, has low resistivity, which makes it an excellent conductor. Glass has high resistivity, which makes it a poor conductor but an excellent insulator. The length and thickness of a conductor also affect its resistivity. A long, thin silver wire has a higher resistivity than a short, thick wire. In addition, the resistivity of a conductor tends to increase as the temperature of the conductor rises and decrease as the temperature of the conductor falls.
Resistivity can be determined using the following formula:
, where the lowercase Greek letter rho (ρ) represents resistivity, R represents resistance of the conductor in ohms (Ω), A represents a cross-sectional area of the conductor in meters squared (m2), and l represents the length of the conductor in meters (m).A good demonstration of resistivity is an average, 60-watt incandescent lightbulb. Inside the bulb is a very thin wire called a filament. The coiled filament wire may look tiny, but if it was straightened, it would be about two meters long (as long as two baseball bats lined up end to end). Although the filament is made of a metal that is a good conductor of electricity, the thinness and long length of the wire increase its resistivity. Collisions between electrons passing through the wire and atoms that make up the wire increase. Each of these collisions produces heat. When the wire heats up enough, it begins to glow, and the bulb produces light.
Conductivity
Conductivity is the reciprocal, or inverse, of resistivity, but it also can be used to determine how well a material conducts electricity. Materials with high conductivity are good conductors, and materials with low conductivity are good insulators. The unit for measuring conductivity is the mho per meter. (Note that "mho" is "ohm" spelled backwards, a further indicator of the inverse relationship between conductivity and resistivity.) The following formula can be used to determine the conductivity of a material:
, where the lowercase Geek letter sigma (σ) represents conductivity and ρ represents resistivity.Bibliography
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