Conductivity and Resistivity - Revision history

Nestifanoes3 at 06:46, 14 April 2025

2025-04-14T06:46:57Z

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	Resistance and area across different fixed points		Resistance and area across different fixed points

			It allows plotting resistance as a function of resistivity, length, or area, while fixing the other two variables. This visualization can help students see how varying a single factor affects the overall resistance. It also allows resistance to be graphed with respect to one of the variables (resistivity, length, or area) across a specified range, keeping the other parameters fixed. It enables intuitive visualization for how geometry and material properties impact resistance.

	Furthermore, [https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html this] external program provides a good visual demonstration of the relationship that acts as a good simulation for altering either the volume, conductance, current, or area of an object to see how the resistance will be altered (but unfortunately the source code is not accessible).		Furthermore, [https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html this] external program provides a good visual demonstration of the relationship that acts as a good simulation for altering either the volume, conductance, current, or area of an object to see how the resistance will be altered (but unfortunately the source code is not accessible).

Nestifanoes3 at 01:14, 14 April 2025

2025-04-14T01:14:43Z

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	'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Islombek Kadirov, Fall 2023''''''		'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Islombek Kadirov, Fall 2023''''''

			Neud Estifanoes Spring 25

	In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.		In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.

Idumitriu3: Undo revision 46278 by Idumitriu3 (talk)

2024-04-15T02:44:20Z

Undo revision 46278 by Idumitriu3 (talk)

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	'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''~~Irene Dumitriu~~, ~~Spring 2024~~''''''		'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Islombek Kadirov, Fall 2023''''''

	In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.		In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.
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	Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.		Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.

	Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the two point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The four-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure the voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistivity with the voltage and resistance where the resistance is the 1/slope of the current vs. voltage graph.

	==Main Idea==		==Main Idea==

Idumitriu3 at 23:55, 14 April 2024

2024-04-14T23:55:18Z

← Older revision		Revision as of 19:55, 14 April 2024
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	'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''~~Islombek Kadirov~~, ~~Fall 2023~~''''''		'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Irene Dumitriu, Spring 2024''''''

	In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.		In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.
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	Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.		Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.

			Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the two point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The four-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure the voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistivity with the voltage and resistance where the resistance is the 1/slope of the current vs. voltage graph.

	==Main Idea==		==Main Idea==

Ikadirov231 at 04:08, 27 November 2023

2023-11-27T04:08:53Z

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	==History==		==History==

	The ~~first scientist to contribute substantially to the~~ study of conductivity and resistivity was Stephen Gray, who with ~~his friend~~ Ganvil Wheler ~~noticed~~ that electricity could be transmitted ~~a distance,~~ and that the ~~effectiveness of this transmission varied~~ between ~~a wire of~~ silk and ~~wire of~~ brass ~~<ref> http://histoires-de-sciences.over-blog.fr/2018/04/history-of-electricity.~~the~~-discovery-of-conductors-and-insulators-by-gray-dufay-and-franklin~~.~~html~~ </~~ref~~>~~. A substantial amount of discovery then followed, including the famous contributions of Benjamin Franklin, but these developments are more relevant to other subjects.~~		<p>The study of conductivity and resistivity has a rich history, marked by significant contributions from various scientists. One of the earliest contributors was Stephen Gray, who along with Ganvil Wheler, observed that electricity could be transmitted over distances and that different materials had varying effectiveness in conducting electricity. This early observation, contrasting the conductivity between silk and brass wires, laid the groundwork for future studies [9].</p>

	~~It was in~~ the ~~early 19th~~ century ~~that the equation for determining resistance from resistivity and geometry was determined by Antoine Becquerel (grandfather to Henri Becquerel, who was a pioneer~~ in ~~radioactivity alongside Marie Skłodowska Curie and Pierre Curie)<ref> https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_83/December_1913/The_History_of_Ohm%27s_Law</ref>. Not long after~~, ~~Georg Ohm proposed an incorrect theorem for~~ the ~~relation between current~~, ~~potential and resistance, then soon amended it~~ to ~~the correct formula. The correction, philosophical differences, and confusion at the time about the definitions~~ of ~~resistance, current and potential led his work~~ to ~~be poorly received at first, but ultimately accepted~~ and ~~celebrated about 15 years after its release~~.		<p>While the 18th century saw notable advancements in understanding electricity, including the work of Benjamin Franklin, these developments were more closely tied to broader aspects of electrical science rather than specifically to conductivity and resistivity.</p>

			<p>The early 19th century marked a pivotal moment in the study of resistivity and conductivity. Antoine Becquerel, the grandfather of Henri Becquerel who later became renowned for his work in radioactivity alongside Marie Skłodowska Curie and Pierre Curie, formulated an equation to determine resistance from resistivity and geometry [10]. This breakthrough provided a more quantitative approach to understanding how electrical resistance was influenced by material properties and structural dimensions.</p>

	<~~ref~~>~~connectedness~~.~~https://science~~.~~jrank.org/pages/2321/Electrical-Conductivity-History.html#:~:text=The%20early%20studies%20of%20electrical~~,~~eighteenth%20and%20early%20nineteenth%20centuries.&text=Georg%20Simon%20Ohm%20(1787%2D1854~~,~~various%20metals%20to%20conduct%20electricity~~. </~~ref~~>		<p>Following Becquerel's work, Georg Ohm, a German physicist, proposed a theorem relating current, potential, and resistance. Although his initial proposition was incorrect, he soon revised it, leading to the formulation of Ohm's law. Despite initial skepticism and poor reception due to philosophical differences and confusion over the definitions of resistance, current, and potential, Ohm's work eventually gained acceptance and recognition, transforming our understanding of electrical resistance and its relationship to current and voltage.</p>
	<~~ref~~>~~https://www~~.~~britannica.com/science/resistivity~~</~~ref~~>
			<p>This period marked a crucial era in the study of electrical properties, as scientists began to establish the fundamental principles that would shape our modern understanding of electrical conductivity and resistivity.</p>

Ikadirov231 at 04:06, 27 November 2023

2023-11-27T04:06:48Z

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	==Connectedness==		==Connectedness==

	Every time an electrical system has been created, an understanding of conductivity and resistivity had to be determined.		<p>Every time an electrical system has been created, an understanding of conductivity and resistivity had to be determined.</p>

	~~since~~ conductivity and resistivity are related, it is reasonable to assume that wires or components with low electric resistivity make good conductors ~~as they have a great~~ ability to transmit electricity and heat ~~and wires or components~~ with high electric resistivity ~~make bad conductors~~.		<p>Since conductivity and resistivity are related, it is reasonable to assume that wires or components with low electric resistivity make good conductors due to their ability to effectively transmit electricity and heat. Conversely, materials with high electric resistivity are less efficient at conducting and are often used as insulators.</p>

	This ~~is important~~ in ~~many~~ real life ~~applications~~, ~~some~~ of ~~which include:~~		<p>This concept has significant applications in real life, including:</p>
			<ul>
			<li><strong>[[Home insulation:]]</strong> Utilizing materials with high resistivity to maintain indoor temperature.</li>
			<li><strong>[[Cooking:]]</strong> Employing pots, pans, and other metallic objects with low resistivity for efficient heat transfer, allowing food to cook evenly without direct exposure to the stove's heat source.</li>
			<li><strong>[[Electronic Devices:]]</strong> Using materials with high resistivity in electronic devices to regulate temperature and prevent overheating, caused by the constant flow of electrical current.</li>
			</ul>

	~~[[Home insulation:]] materials with high resistivity so the temperature of your house is maintained.~~

	[[Cooking:]] Pots, pans, and other metallic objects are used to cook food. This is because the food is placed on the pan, which due to its low resistivity resulting from the metal's free electrons. As the resistivity is low, there is high conductivity and the heat from a stove would be able to easily reach the food on the pan without having to place the food directly onto the stove's surface.

	[[Electronic Devices:]] Electronic devices rely on the transportation of currents to create electricity that powers the device. However, one problem with many electronic devices is they are prone to overheating. In order to regulate the temperature created by the constant usage of energy in the device, materials in the machine can be surrounded or replaced with highly resistive materials to slow the conductance of the current.

	[[Measuring Conductivity]]		[[Measuring Conductivity]]

Ikadirov231 at 04:02, 27 November 2023

2023-11-27T04:02:43Z

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	'''Example Number 2'''		'''Example Number 2'''

	A unknown material is used in the creation of a video game console.		An unknown material is used in the creation of a video game console.

	Part A: How would the amount of free electrons in the material affect the conductance of the material?		Part A: How would the amount of free electrons in the material affect the conductance of the material?

	Part B:Would the ~~materials~~ conductance increase or decrease if you put the material in the freezer as opposed to room temperature?		Part B: Would the material's conductance increase or decrease if you put the material in the freezer as opposed to room temperature?

	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
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	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

			The conductance of a material is directly influenced by the number of free electrons available for conduction. A higher number of free electrons implies lower resistance, as conductance is inversely related to resistivity (<math> \sigma = \frac{1}{\rho} </math>). Therefore, an increase in free electrons results in higher conductance.

	Because the more free electrons, the less resistance a material has and since <math> \sigma = \frac{1}{\rho} </math>, there is an obvious inverse relationship between resistivity and conductance. This means that the more free electrons, the less resistance, and therefore the more conductance an object will have.
	</div></div>		</div></div>


	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
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	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

	~~Temperature~~ increases ~~cause~~ free ~~electrons~~ to ~~move quicker~~ in ~~any~~ material.		Lowering the temperature of a material typically increases its resistivity, as free electron movement is slowed. This results in a decrease in conductance. In colder environments (like a freezer), the slowed electron movement leads to increased resistance and consequently, decreased conductance in the material.

	If free electrons move quicker, the resistance of the object decreases and the conductance of the material would increase. This implies that the material will transfer heat and or energy slower because the material was moved to a colder environment, decreasing the speed of the free electrons, increasing resistivity, and decreasing conductance of the material.
	</div></div>		</div></div>

Ikadirov231 at 03:58, 27 November 2023

2023-11-27T03:58:32Z

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	<math> \sigma = \frac{1}{\rho} = \frac{1}{200 \; \Omega \cdot m} = 0.005 \frac{1}{\Omega \cdot m} </math>		<math> \sigma = \frac{1}{\rho} = \frac{1}{200 \; \Omega \cdot m} = 0.005 \frac{1}{\Omega \cdot m} </math>

			</div></div>

			'''Example Number 1.2'''

			A copper wire has a resistivity of <math> 1.68 \times 10^{-8} \; \Omega\cdot m </math> at room temperature. Determine its conductivity.

			<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
			<div style="font-weight:bold;line-height:1.6;">Solution</div>
			<div class="mw-collapsible-content">

			Given that conductivity is the inverse of resistivity,

			<math> \sigma = \frac{1}{\rho} = \frac{1}{1.68 \times 10^{-8} \; \Omega \cdot m} = 5.95 \times 10^{7} \frac{1}{\Omega \cdot m} </math>

			This result indicates high conductivity, characteristic of copper.

			</div></div>

			'''Example Number 1.3'''

			Calculate the resistivity of an aluminum material with a conductivity of <math> 3.5 \times 10^{7} \frac{1}{\Omega \cdot m} </math>.

			<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
			<div style="font-weight:bold;line-height:1.6;">Solution</div>
			<div class="mw-collapsible-content">

			Since resistivity is the reciprocal of conductivity,

			<math> \rho = \frac{1}{\sigma} = \frac{1}{3.5 \times 10^{7} \frac{1}{\Omega \cdot m}} = 2.86 \times 10^{-8} \; \Omega\cdot m </math>

			This value of resistivity is typical for aluminum.

	</div></div>		</div></div>

Ikadirov231 at 03:55, 27 November 2023

2023-11-27T03:55:08Z

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	As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>		As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>

	~~Naturally~~, ~~this is exactly the scenario present in~~ a standard wire~~. The next two relevant equations are two statements~~ of ~~the same fact, which we call~~ Ohm's law~~. Precisely, it governs~~ the ~~relationship~~ between the flow of charge and the electric field ~~which produces that~~ flow. ~~The first form states this explicitly~~:		<p>In the realm of electrical engineering, a standard wire exemplifies a practical application of Ohm's Law. This fundamental law delineates the correlation between the flow of electric charge and the electric field responsible for this flow. Ohm's Law is articulated through two essential equations:</p>

			<p>The first equation explicitly states the relationship:</p>

	~~Through this equation, the "skin effect" is produced.~~		<math>\vec{J} = \sigma \vec{E}</math>

	The ~~[["skin effect"]] consists~~ of ~~an explanation for the relationship between the~~ current density ~~and~~ the ~~radius~~ of a ~~wire~~. ~~It explains~~ that ~~the thicker the wire (the bigger the radius), the larger the~~ current density.		<p>Here, <math>\vec{J}</math> represents the current density, and <math>\vec{E}</math> signifies the electric field. The concept of current density refers to the amount of charge traversing a specified cross-sectional area within a certain time frame, measured in SI units as <math>\frac{A}{m^2} = \frac{C}{m^2 \cdot s}</math>. This elucidates that current density is a 'density' with 'area' in its denominator.</p>

	<~~math~~> ~~\vec{J} = \sigma \vec{E}~~ </~~math~~>		<p>Another aspect related to Ohm's Law is the "skin effect," which elucidates the interplay between current density and the radius of a wire. It posits that a larger wire radius leads to increased current density. This effect is integral to understanding Ohm's Law in practical scenarios.</p>

	~~Here~~ <~~math~~> \vec{J} </math> is the current density, and <math> \vec{E} </math> is the electric field as we've seen before. An aside on current density: it is the amount of charge which passes through a given cross sectional area in a given period of time, with SI units <math> \frac{A}{m^2} = \frac{C}{m^2 \cdot s} </math>. This means that it is a ''density'' with ''area'' in the denominator, which can be confusing. Given what one has learned so far, this is the operable definition of Ohm's Law~~. However, another version~~ is ~~more frequently used later on, and so will also be given here~~:		<p>Another commonly used form of Ohm's Law is expressed as:</p>

	<math> V = I R </math>		<math>V = I R</math>

			<p>Where <math>V</math> is the electric potential, <math>I</math> the current, and <math>R</math> the resistance. This version of the law is widely employed in various electrical engineering applications.</p>

	~~where <math> V </math> is the electric potential, <math> I </math> is the current, and <math> R </math> is resistance as defined before.~~

Ikadirov231 at 03:52, 27 November 2023

2023-11-27T03:52:26Z

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	An insulator is a material that exhibits high resistance to the flow of electric current, effectively preventing or significantly hindering the passage of electricity. Semiconductors, on the other hand, are materials that possess properties of both conductors and insulators, allowing them to conduct electricity under certain conditions. Common examples of conductive materials include metals, known for their low resistivity and high conductivity. Insulators typically comprise materials like wood or plastics, which have high resistivity and are used to prevent unwanted flow of electric current <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html </ref>. Semiconductors, though more rare compared to conductors and insulators, play a crucial role in modern technology, particularly in the construction of transistors. These components are essential in all computers and a wide range of electronic devices. The most commonly used semiconductor material is doped silicon, which, through the process of doping, acquires the necessary electrical properties to efficiently control and amplify electronic signals. This characteristic makes semiconductors indispensable in the realm of digital electronics and integrated circuits <ref> https://electronics.howstuffworks.com/diode.htm </ref>. Beyond conductors, insulators, and semiconductors, there is another notable category known as superconductors. ~~These~~ unique materials exhibit zero electrical resistance under specific conditions, typically at extremely low temperatures and/or under high pressures <ref> https://home.cern/science/engineering/superconductivity </ref>, and there also exist a host of other materials with odd behaviors.		An insulator is a material that exhibits high resistance to the flow of electric current, effectively preventing or significantly hindering the passage of electricity. Semiconductors, on the other hand, are materials that possess properties of both conductors and insulators, allowing them to conduct electricity under certain conditions. Common examples of conductive materials include metals, known for their low resistivity and high conductivity. Insulators typically comprise materials like wood or plastics, which have high resistivity and are used to prevent unwanted flow of electric current <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html </ref>. Semiconductors, though more rare compared to conductors and insulators, play a crucial role in modern technology, particularly in the construction of transistors. These components are essential in all computers and a wide range of electronic devices. The most commonly used semiconductor material is doped silicon, which, through the process of doping, acquires the necessary electrical properties to efficiently control and amplify electronic signals. This characteristic makes semiconductors indispensable in the realm of digital electronics and integrated circuits <ref> https://electronics.howstuffworks.com/diode.htm </ref>. Beyond conductors, insulators, and semiconductors, there is another notable category known as superconductors. The phenomenon of superconductivity, discovered in 1911, is a quantum mechanical marvel that allows for the unimpeded flow of electric current, making superconductors highly valuable for applications requiring efficient energy transmission, powerful electromagnets, and advanced technologies like magnetic resonance imaging (MRI) and particle accelerators, and these unique materials exhibit zero electrical resistance under specific conditions, typically at extremely low temperatures and/or under high pressures <ref> https://home.cern/science/engineering/superconductivity </ref>, and there also exist a host of other materials with odd behaviors.


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	[[Factors that influence the resistivity of an object:]]		[[Factors that influence the resistivity of an object:]]

	~~~temperature the material is held in~~		~Material Composition: Different materials inherently have different levels of resistivity. For instance, metals typically have lower resistivity than insulators like plastic or wood.

	~~~concentrations of ions (an electrolyte moves through water carrying electrical currents~~.		~Temperature: Generally, for conductors, resistivity increases with temperature. In semiconductors and insulators, the effect can be more complex.

	~~~type~~ of ~~ions~~		~Impurities and Material Defects: The presence of impurities and defects in a material can significantly alter its resistivity. This is particularly notable in semiconductors, where doping with impurities is used to control resistivity.
	~~<ref>https://aperainst~~.~~com/blog/cat/Conductivity%2C+TDS%2C+Salinity%2C+Resistivity/#:~:text=There%20are%20three%20main%20factors~~,~~and%20can%20move%20through%20water~~.~~</ref>~~

	~ ~~if rock~~, ~~pore saturation~~		~ Physical Structure: The microscopic structure of a material, including its crystal structure and the presence of grain boundaries, can affect resistivity.

			~Pressure: Applying pressure to a material can change its resistivity, though this effect is generally less significant than temperature or material composition.


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	===Mathematical Method===		===Mathematical Method===

	~~First, we have the relation~~ between conductivity and resistivity:		The relationship between conductivity and resistivity is a fundamental concept in the field of materials science and electrical engineering. Here's how they are related:


	<math> \sigma = \frac{1}{\rho} </math>		<math> \sigma = \frac{1}{\rho} </math>
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	[[File:Resistivity geometry.svg\|Resistivity geometry\|300 px\|right]]		[[File:Resistivity geometry.svg\|Resistivity geometry\|300 px\|right]]

	Conductivity and Resistivity are properties ~~of a material~~, ~~dependent~~ primarily ~~on its~~ chemical composition and ~~structure~~, but also ~~on its~~ temperature and other environmental ~~factors~~. ~~As such~~, ~~for our purposes it will always be~~ either ~~a know value, plugged into an equation,~~ or ~~an unknown value,~~ derived from that equation~~. Our interest is therefore~~ in ~~those equations~~. ~~The first~~ is on the ~~idealized relation between resistivity~~ and ~~resistance:~~		Conductivity and Resistivity are intrinsic material properties, influenced primarily by chemical composition and structural attributes, but also sensitive to temperature and other environmental conditions. In practical applications, these values are either predetermined constants used in calculations or derived outcomes from specific equations. The focus thus lies in understanding the relevant equations that govern these properties. A key equation relates resistivity to resistance in an idealized manner, providing a foundational understanding for analyzing the electrical characteristics of different materials. This relationship is crucial for the design and analysis of electrical and electronic systems, where accurate knowledge of material properties is essential.

	<math> R = \frac{\rho L}{A} </math>		<math> R = \frac{\rho L}{A} </math>


	In this, resistance is <math> R </math>, the length of the wire is <math> L </math>, <math> rho </math> is equal to resistivity and the variable <math>A </math> is its cross sectional area. This ~~assumes that there is~~ a ~~clearly~~ defined length ~~(parallel to~~ the direction of current flow) and cross sectional area (perpendicular to the direction of ~~current flow)~~.		In this context, the resistance of a wire is denoted as <math> R </math>, the length of the wire is <math> L </math>, <math> rho </math> is equal to resistivity and the variable <math>A </math> is its cross sectional area. This formulation presupposes a well-defined length of the wire aligned with the direction of electric current flow and a specific cross-sectional area perpendicular to the current's direction. These parameters are essential in determining the wire's resistance characteristics, especially in the context of electrical and electronic engineering.

	~~Area~~ of a conductor can be ~~adjusted~~ by making additional connections to ~~the conductor in~~ a circuit. For ~~example~~, ~~If you had~~ a current ~~pointing~~ from North to South, by attaching a second conductor parallel to the first ~~one~~ the area. of the ~~conductor would be doubled~~.		Adjusting the area of a conductor can be achieved by making additional connections to it within a circuit. For instance, if there is a current flowing from North to South through a conductor, attaching a second conductor parallel to the first effectively doubles the area of the conductor. This modification impacts the overall resistance of the circuit, as the cross-sectional area is a key factor in determining resistance. By increasing the area through parallel connections, the resistance is reduced, allowing more current to flow through the circuit.

	As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>		As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>