Steady State - Revision history

Vtadakamalla3: Undo revision 47986 by Vtadakamalla3 (talk)

2026-04-25T04:44:03Z

Undo revision 47986 by Vtadakamalla3 (talk)

← Older revision		Revision as of 00:44, 25 April 2026
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	'''Claimed ~~Vivan Tadakamalla~~ (Spring ~~2026~~)'''		'''Claimed Alex Dulisse (Spring 2018)'''

	Imagine a circuit in which the only battery has been disconnected. In such a setup there would be no electric field in the circuit and therefore no moving charges so the circuit would be in static equilibrium. When the battery is reconnected, an electric field will quickly propagate through the circuit and the charges in the circuit will accelerate. After a short time, the charges will move at a constant speed through the circuit and the electric field at each part of the circuit will remain unchanged. This means that at any given moment, all properties of the circuit remain unchanged even though an electric field is acting on the charges. At this time, when the state of the circuit does not change with the passage of time, the circuit is said to be in '''steady state.'''		Imagine a circuit in which the only battery has been disconnected. In such a setup there would be no electric field in the circuit and therefore no moving charges so the circuit would be in static equilibrium. When the battery is reconnected, an electric field will quickly propagate through the circuit and the charges in the circuit will accelerate. After a short time, the charges will move at a constant speed through the circuit and the electric field at each part of the circuit will remain unchanged. This means that at any given moment, all properties of the circuit remain unchanged even though an electric field is acting on the charges. At this time, when the state of the circuit does not change with the passage of time, the circuit is said to be in '''steady state.'''

Vtadakamalla3 at 04:30, 25 April 2026

2026-04-25T04:30:52Z

← Older revision		Revision as of 00:30, 25 April 2026
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	'''Claimed ~~Alex Dulisse~~ (Spring ~~2018~~)'''		'''Claimed Vivan Tadakamalla (Spring 2026)'''

	Imagine a circuit in which the only battery has been disconnected. In such a setup there would be no electric field in the circuit and therefore no moving charges so the circuit would be in static equilibrium. When the battery is reconnected, an electric field will quickly propagate through the circuit and the charges in the circuit will accelerate. After a short time, the charges will move at a constant speed through the circuit and the electric field at each part of the circuit will remain unchanged. This means that at any given moment, all properties of the circuit remain unchanged even though an electric field is acting on the charges. At this time, when the state of the circuit does not change with the passage of time, the circuit is said to be in '''steady state.'''		Imagine a circuit in which the only battery has been disconnected. In such a setup there would be no electric field in the circuit and therefore no moving charges so the circuit would be in static equilibrium. When the battery is reconnected, an electric field will quickly propagate through the circuit and the charges in the circuit will accelerate. After a short time, the charges will move at a constant speed through the circuit and the electric field at each part of the circuit will remain unchanged. This means that at any given moment, all properties of the circuit remain unchanged even though an electric field is acting on the charges. At this time, when the state of the circuit does not change with the passage of time, the circuit is said to be in '''steady state.'''

Daniel72: /* Middling */ The equation & solution for the cross-sectional area of the wire were incorrect. Even though the correct value was used later.

2023-11-11T16:24:51Z

Middling: The equation & solution for the cross-sectional area of the wire were incorrect. Even though the correct value was used later.

← Older revision		Revision as of 12:24, 11 November 2023
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	<br><math>n= 8.342\times 10^{28}e−/m^3</math>		<br><math>n= 8.342\times 10^{28}e−/m^3</math>
	<br>The cross-sectional area of the wire is		<br>The cross-sectional area of the wire is
	<math>A= \pi r^2 = \pi(2.053\times10^{−3}m^2) = 23.~~310~~ \times 10^{–6}m^2</math>		<math>A= \pi r^2 = \pi(2.053\times0.5\times10^{−3})^2 = 3.3103 \times 10^{–6}m^2</math>

	<br>Rearranging <math>I= \left \| q \right \|nA\bar{v}</math> to isolate drift velocity gives you:		<br>Rearranging <math>I= \left \| q \right \|nA\bar{v}</math> to isolate drift velocity gives you:

Sydney: /* The Main Idea */

2019-08-26T00:01:48Z

The Main Idea

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 Each of these bullets is a different way of saying the same thing, that the state of the circuitry acting on any charges remains unchanged with respect to time. It is important to remember that a circuit being in steady state does not mean that the drift speed is the same every where in the circuit, only that it is unchanging for each specific location in the circuit. Also, a circuit in which there is no current may still be in steady state (such as an RC circuit in which the capacitors are fully charged), as long as there is still a constant electric field in all conductive parts of the circuit.
-===A Mathematical Model===
+'''A Conceptual Understanding'''
 For charges to move through the circuit, there must be an applied electric field that causes the mobile charges to move. Since there cannot be excess charge in the interior of a conductor, the surface charges must be producing the electric field. This electric field must be parallel to the wire because of the properties of a conductor. In a conductor, mobile charges always move to cancel out an electric field, meaning that the only electric field in the circuit must be parallel to the direction of current flow.
@@ Line 52: / Line 22: @@
 [[File:Wire_Charges2.png|thumb = Wire_Charges2.png|upright=0.1|400px|center|Surface Charge Distribution]]
-===Steady State vs. Other States===
+'''Steady State vs. Other States'''
 When circuits move from static equilibrium to steady state, they typically do so in a very small amount of time. However, the [[Non Steady State]], or Transient State, which takes place in between, is an important aspect of circuits. When a circuit is in the Non Steady State, over time its state will approach the steady state. After enough time has elapsed, the difference is so slim that the circuit can be considered to be in steady state, even though in theory it never quite reaches steady state. The equations to model Non Steady States are different depending on the type of circuit being analyzed.
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 |-
 |}
 ==Examples==

Sydney: /* See also */

2019-08-25T23:59:27Z

Sydney: /* Solutions */

2019-08-25T23:51:14Z

Solutions

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 <br><math>E_{thick}=2.28 V/m</math>
 <br>We know that <math>\bar{v}=\mu \left | E_{applied} \right |</math>.
 <br>The drift velocity of the thin wire is <math>\bar{v}=\mu E_{thin} = [0.0006 (m/s)/(V/m)][3.5 V/m]=  2.10 \times 10^{–3} m/s</math>.

Sydney: /* Examples */

2019-08-25T23:50:52Z

Examples

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 ==Examples==
-===Simple Problem===
+===Simple===
 What are the values of X and Y in the following circuit?
 [[Image:Node_rule_simple_problem.png|thumbnail = Node_rule_simple_problem.png|upright=0.5|frame|center|Node Rule]]
-===Middling Problem===
+'''Solution'''
 [http://cnx.org/contents/Ax2o07Ul@9.39:3ct4v3c5@4/Current| (Example taken from the OpenStax College Physics Textbook)]
 Calculate the drift velocity of electrons in a 12-gauge copper wire (which has a diameter of '''2.053 mm''') carrying a '''20.0-A''' current, given that there is one free electron per copper atom. The density of copper is <math>8.80\times 10^{3} kg/m^3</math>.
 A circuit made of two wires is in the steady state. The battery has an emf of '''1.5 V'''. Both wires are length '''25 cm''' and made of the same material. The thin wire's diameter is '''0.25 mm''', and the thick wire's diameter is '''0.31 mm'''. There are <math>4\times 10^{28}</math> mobile electrons per cubic meter of this material, and the electron mobility of this material is '''0.0006 (m/s)/(V/m)'''.
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 [[File:sscircuit2.png]]
 ====Solutions====

Sydney: /* A Conceptual Understanding */

2019-08-24T20:32:42Z

A Conceptual Understanding

← Older revision		Revision as of 16:32, 24 August 2019
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	===A Conceptual Understanding===		===A Conceptual Understanding===

	For charges to move through the circuit, there must be an applied electric field that causes the mobile charges to move. Since ~~the~~ cannot be excess charge in the interior of a conductor, the surface charges must be producing the electric field. This electric field must be parallel to the wire because of the properties of a conductor. In a conductor, mobile charges always move to cancel out an electric field, meaning that the only electric field in the circuit must be parallel to the direction of current flow.		For charges to move through the circuit, there must be an applied electric field that causes the mobile charges to move. Since there cannot be excess charge in the interior of a conductor, the surface charges must be producing the electric field. This electric field must be parallel to the wire because of the properties of a conductor. In a conductor, mobile charges always move to cancel out an electric field, meaning that the only electric field in the circuit must be parallel to the direction of current flow.
	It is also important to conceptually understand why this electric field eventually reaches steady state. When a battery is first connected to a circuit, the electric field increases in magnitude, the rate at which the charges move through the circuit increases in magnitude too. As charges move through the circuit, there is a drag force in the opposite direction of their motion (similar to friction) known as the resistance of the wire. Since <math>I=V/R</math>, eventually these opposing forces will be equal in magnitude, bringing the circuit to steady state. Once a circuit is described as being in the steady state, there must be a constant electric field in the wire, the electric field has uniform magnitude throughout wire sections with similar cross-sectional area, and the electric field is parallel to the wire at every location along the wire.		It is also important to conceptually understand why this electric field eventually reaches steady state. When a battery is first connected to a circuit, the electric field increases in magnitude, the rate at which the charges move through the circuit increases in magnitude too. As charges move through the circuit, there is a drag force in the opposite direction of their motion (similar to friction) known as the resistance of the wire. Since <math>I=V/R</math>, eventually these opposing forces will be equal in magnitude, bringing the circuit to steady state. Once a circuit is described as being in the steady state, there must be a constant electric field in the wire, the electric field has uniform magnitude throughout wire sections with similar cross-sectional area, and the electric field is parallel to the wire at every location along the wire.

	[[File:Wire_Charges2.png\|thumb = Wire_Charges2.png\|upright=0.1\|~~100px~~\|center~~\|frame~~\|Surface Charge Distribution]]		[[File:Wire_Charges2.png\|thumb = Wire_Charges2.png\|upright=0.1\|400px\|center\|Surface Charge Distribution]]

	===Steady State vs. Other States===		===Steady State vs. Other States===

Sydney: /* A Mathematical Model */

2019-08-24T20:19:31Z

A Mathematical Model

← Older revision		Revision as of 16:19, 24 August 2019
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	This is called the “[[Node Rule]].” All this is saying is that exactly what enters the node must exit. In other words, charge dose not disappear or come into existence just because one wire splits in two.		This is called the “[[Node Rule]].” All this is saying is that exactly what enters the node must exit. In other words, charge dose not disappear or come into existence just because one wire splits in two.

	[[Image:NodeRule2.jpg\|thumbnail = NodeRule2.jpg\|upright=0.5\|~~frame~~\|center\|Node Rule]]		[[Image:NodeRule2.jpg\|thumbnail = NodeRule2.jpg\|upright=0.5\|400 px\|center\|Node Rule]]

	===A Conceptual Understanding===		===A Conceptual Understanding===

Sydney: /* A Mathematical Model */

2019-08-24T20:18:21Z

A Mathematical Model

← Older revision		Revision as of 16:18, 24 August 2019
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	===A Mathematical Model===		===A Mathematical Model===
	'''Current'''		'''Current'''

	There are two ways to describe current in a circuit, the electron current (<math>i</math>), and the conventional current (<math>I</math>). Electron current describes the motion of charges as it actually happens in the circuit: electrons moving through the conductor. Conventional current has the same magnitude and opposite direction as electron current as it describes positive charges moving through a circuit. Although circuits will sometimes act like positive charges are moving through the circuit if there are “electron holes,” it is important to understand that there are not positively charged particles moving through circuits. Even though it is backwards from the physical reality, conventional current is more commonly used because the motion of electrons in circuits was not understood when the first discoveries of electricity were made.		There are two ways to describe current in a circuit, the electron current (<math>i</math>), and the conventional current (<math>I</math>). Electron current describes the motion of charges as it actually happens in the circuit: electrons moving through the conductor. Conventional current has the same magnitude and opposite direction as electron current as it describes positive charges moving through a circuit. Although circuits will sometimes act like positive charges are moving through the circuit if there are “electron holes,” it is important to understand that there are not positively charged particles moving through circuits. Even though it is backwards from the physical reality, conventional current is more commonly used because the motion of electrons in circuits was not understood when the first discoveries of electricity were made.
	The following formulas can be used to describe electron and conventional current, respectively:		The following formulas can be used to describe electron and conventional current, respectively:
	<br><math>i= nA\bar{v}</math>		<br><math>i= nA\bar{v}</math>

	<math>I= \left \| q \right \|nA\bar{v}</math>		<math>I = \left \| q \right \|nA\bar{v}</math>

	n = charge density, the number of charged particles per unit volume		n = charge density, the number of charged particles per unit volume
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	v = drift speed, the speed at which mobile charges move through a section of wire		v = drift speed, the speed at which mobile charges move through a section of wire

	q=charge of the mobile particles being described (only matters for conventional current)		q = charge of the mobile particles being described (only matters for conventional current)

	Keep in mind that drift velocity <math>\bar{v}=\mu \left \| E_{applied} \right \|</math>		Keep in mind that drift velocity <math>\bar{v}=\mu \left \| E_{applied} \right \|</math>
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	'''Kirchoff's Node Rule'''		'''Kirchoff's Node Rule'''

	When a wire splits in to two, this junction is referred to as a node. Current flowing through the node must follow the equation <math>\Sigma I_{in} = \Sigma I_{out}</math>.		When a wire splits in to two, this junction is referred to as a node. Current flowing through the node must follow the equation <math>\Sigma I_{in} = \Sigma I_{out}</math>.
	This is called the “[[Node Rule]].” All this is saying is that exactly what enters the node must exit. In other words, charge dose not disappear or come into existence just because one wire splits in two.		This is called the “[[Node Rule]].” All this is saying is that exactly what enters the node must exit. In other words, charge dose not disappear or come into existence just because one wire splits in two.

← Older revision		Revision as of 19:59, 25 August 2019
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	== See also ==		== See also ==
			===Further Reading===
	* [[Current]]		* [[Current]]
	* [[Fundamentals of Resistance]]		* [[Fundamentals of Resistance]]
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	* [[Series Circuits]]		* [[Series Circuits]]
	* [[Parallel Circuits]]		* [[Parallel Circuits]]
			===External Links===
			* https://www.youtube.com/watch?v=Byvz0MMH_fw
			* https://www.amherst.edu/system/files/media/1182/Lecture15%252520slides.pdf

	==References==		==References==