Non Steady State - Revision history

Sydney: /* =A Mathematical Model+ */

2019-09-01T03:58:31Z

=A Mathematical Model+

← Older revision		Revision as of 23:58, 31 August 2019
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	Non-steady state circuits are specifically important when analyzing the charging or discharging a capacitor. Surely, when a capacitor fully charged (Q/C = Emf) or fully discharged (Q=0), the circuit is in steady state — the derivative of charge with respect to time is 0.		Non-steady state circuits are specifically important when analyzing the charging or discharging a capacitor. Surely, when a capacitor fully charged (Q/C = Emf) or fully discharged (Q=0), the circuit is in steady state — the derivative of charge with respect to time is 0.

	===A Mathematical Model+==		===A Mathematical Model===

	The main two facets of non-steady state circuits, for the purposes of this course, cover the charging and discharging of capacitors. Mathematically, an exponential change occurs when the derivative of a quantity has a relation to the quantity itself. We'll be applying this to the charge and discharge of capacitors, with varying circuit arrangements dependent on switches. Note that throughout these examples, we'll be using the Loop Rule (more formally known as the Kirchoff's Voltage Rule) -- but not in terms of steady state. That is, the more familiar variation (∆Vloop = 0) doesn't apply in this case, as it details the circuit at the endpoints of the timeframe, or steady state. Through these few examples, we'll be looking at the intermediate moments of a given time frame.		The main two facets of non-steady state circuits, for the purposes of this course, cover the charging and discharging of capacitors. Mathematically, an exponential change occurs when the derivative of a quantity has a relation to the quantity itself. We'll be applying this to the charge and discharge of capacitors, with varying circuit arrangements dependent on switches. Note that throughout these examples, we'll be using the Loop Rule (more formally known as the Kirchoff's Voltage Rule) -- but not in terms of steady state. That is, the more familiar variation (∆Vloop = 0) doesn't apply in this case, as it details the circuit at the endpoints of the timeframe, or steady state. Through these few examples, we'll be looking at the intermediate moments of a given time frame.
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	~~===~~Example 1: Charging a Capacitor~~===~~		'''Example 1: Charging a Capacitor'''

	To better understand this, let’s take a look at a simple RC circuit consisting of a battery '''''Emf''''', a resistor of resistance '''''R''''', and a capacitor with a capacitance '''''C'''''.		To better understand this, let’s take a look at a simple RC circuit consisting of a battery '''''Emf''''', a resistor of resistance '''''R''''', and a capacitor with a capacitance '''''C'''''.
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	----		----

	~~===~~Example 2: Discharging a Capacitor~~===~~		'''Example 2: Discharging a Capacitor'''

	Very similar to charging a capacitor, the discharging of a capacitor involves a time period when the derivatives of charge and current are nonzero. The given circuit is once again in non-steady state.		Very similar to charging a capacitor, the discharging of a capacitor involves a time period when the derivatives of charge and current are nonzero. The given circuit is once again in non-steady state.
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	[[File:NSScircuit2.png]]		[[File:NSScircuit2.png]]

	Consider the same circuit ~~below~~. Assume ~~the switch~~ the switch was at location '''''X''''' for a very long time, and the capacitor is fully charged.		Consider the same circuit above. Assume the switch was at location '''''X''''' for a very long time, and the capacitor is fully charged.

	The moment the switch is moved to location '''''Z''''', the capacitor supplies a voltage, with an '''''Emf''''' equal to that of the battery. As current begins to flow, the charges on the plates grow increasingly smaller with time. Because of this, both the capacitor’s voltage and the current flowing through the circuit are also decreasing.		The moment the switch is moved to location '''''Z''''', the capacitor supplies a voltage, with an '''''Emf''''' equal to that of the battery. As current begins to flow, the charges on the plates grow increasingly smaller with time. Because of this, both the capacitor’s voltage and the current flowing through the circuit are also decreasing.

Sydney: /* Conceptual Review */

2019-09-01T03:53:44Z

Conceptual Review

← Older revision		Revision as of 23:53, 31 August 2019
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	[[File:9i.~~gif~~]]		[[File:non steady state image.png\|400 px]]

Sydney: /* Mathematical Applications */

2019-09-01T03:31:23Z

Mathematical Applications

← Older revision		Revision as of 23:31, 31 August 2019
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	Non-steady state circuits are specifically important when analyzing the charging or discharging a capacitor. Surely, when a capacitor fully charged (Q/C = Emf) or fully discharged (Q=0), the circuit is in steady state — the derivative of charge with respect to time is 0.		Non-steady state circuits are specifically important when analyzing the charging or discharging a capacitor. Surely, when a capacitor fully charged (Q/C = Emf) or fully discharged (Q=0), the circuit is in steady state — the derivative of charge with respect to time is 0.

	==Mathematical ~~Applications~~==		===A Mathematical Model+==

	The main two facets of non-steady state circuits, for the purposes of this course, cover the charging and discharging of capacitors. Mathematically, an exponential change occurs when the derivative of a quantity has a relation to the quantity itself. We'll be applying this to the charge and discharge of capacitors, with varying circuit arrangements dependent on switches. Note that throughout these examples, we'll be using the Loop Rule (more formally known as the Kirchoff's Voltage Rule) -- but not in terms of steady state. That is, the more familiar variation (∆Vloop = 0) doesn't apply in this case, as it details the circuit at the endpoints of the timeframe, or steady state. Through these few examples, we'll be looking at the intermediate moments of a given time frame.		The main two facets of non-steady state circuits, for the purposes of this course, cover the charging and discharging of capacitors. Mathematically, an exponential change occurs when the derivative of a quantity has a relation to the quantity itself. We'll be applying this to the charge and discharge of capacitors, with varying circuit arrangements dependent on switches. Note that throughout these examples, we'll be using the Loop Rule (more formally known as the Kirchoff's Voltage Rule) -- but not in terms of steady state. That is, the more familiar variation (∆Vloop = 0) doesn't apply in this case, as it details the circuit at the endpoints of the timeframe, or steady state. Through these few examples, we'll be looking at the intermediate moments of a given time frame.
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	It’s interesting to note that if the resistor were, for example, a lightbulb, the exponential decay of the current passing through the lightbulb would inevitably cause the lightbulb to shine its brightest at time '''''t=0''''', and grow increasingly dimmer as the capacitor discharges. When the capacitor is fully discharged, as mentioned above, the current will be 0, and the lightbulb will go out.		It’s interesting to note that if the resistor were, for example, a lightbulb, the exponential decay of the current passing through the lightbulb would inevitably cause the lightbulb to shine its brightest at time '''''t=0''''', and grow increasingly dimmer as the capacitor discharges. When the capacitor is fully discharged, as mentioned above, the current will be 0, and the lightbulb will go out.


	==Conceptual Review==		==Conceptual Review==

Sydney at 00:20, 26 August 2019

2019-08-26T00:20:05Z

← Older revision		Revision as of 20:20, 25 August 2019
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	by Javier Rodriguez		by Javier Rodriguez

	~~----~~		==The Main Idea==

	RC circuits in non-steady state are defined by changing charges, currents, and voltages as a function of time.		RC circuits in non-steady state are defined by changing charges, currents, and voltages as a function of time.

Sydney at 00:16, 26 August 2019

2019-08-26T00:16:52Z

← Older revision		Revision as of 20:16, 25 August 2019
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	Because R is given, we can divide I by R to get 500 V / 300 Ohms = 1.67 A.		Because R is given, we can divide I by R to get 500 V / 300 Ohms = 1.67 A.

			==Connectedness==

			This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.

	== See also ==		== See also ==
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	Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press		Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press

	==~~Connectedness~~==		===External links===

	This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.

	=~~=External links==~~		"RC Circuits Charging" (https://www.youtube.com/watch?v=OwbQLrNBDpY)

	~~"RC Circuits Charging" (https://www.youtube.com/watch?v=OwbQLrNBDpY)~~
	"RC Circuits Charging and Discharging Calculations" (https://www.youtube.com/watch?v=JHHikLqJuYk)		"RC Circuits Charging and Discharging Calculations" (https://www.youtube.com/watch?v=JHHikLqJuYk)

	"RC Circuits, Charging Capacitors, Discharing Capactiors and Equations" (https://www.youtube.com/watch?v=6Kz2xas_vOE)		"RC Circuits, Charging Capacitors, Discharing Capactiors and Equations" (https://www.youtube.com/watch?v=6Kz2xas_vOE)

Sydney: /* Further reading and Connectedness. */

2019-08-26T00:14:27Z

Kcrawford32: /* Conceptual Review */

2016-04-12T06:10:06Z

Conceptual Review

← Older revision		Revision as of 02:10, 12 April 2016
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	[[File:9i.~~jpeg~~]]		[[File:9i.gif]]

Kcrawford32: /* Conceptual Review */

2016-04-12T06:06:39Z

Conceptual Review

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 B. B. at a maximum and decreasing
 (1) Initially there is no charge on the capacitor and hence no voltage drop across it. All of the potential drop is across the resistor – maximum current. As charge builds up on the capacitor the current will “slow down” – there will be a smaller drop across the resistor and hence less current.
 == See also ==

Jrod1096 at 01:42, 1 December 2015

2015-12-01T01:42:34Z

← Older revision		Revision as of 21:42, 30 November 2015
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	*Current		*Current
	*Ohm's Law		*Ohm's Law


	==Further reading and Connectedness.==		==Further reading and Connectedness.==
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	This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.		This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.

	Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press		'''Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press'''

	==External links==		==External links==

Jrod1096 at 01:42, 1 December 2015

2015-12-01T01:42:08Z

← Older revision		Revision as of 21:42, 30 November 2015
Line 123:		Line 123:


	===Further reading and Connectedness.===		==Further reading and Connectedness.==

	This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.		This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.
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	Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press		Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press

	===External links===		==External links==

	"RC Circuits Charging" (https://www.youtube.com/watch?v=OwbQLrNBDpY)		"RC Circuits Charging" (https://www.youtube.com/watch?v=OwbQLrNBDpY)

← Older revision		Revision as of 20:14, 25 August 2019
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	*Ohm's Law		*Ohm's Law

	==Further reading ~~and~~ Connectedness.==		===Further reading===

			Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press

			==Connectedness==

	This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.		This topic is particularly relevant to Electrical and Computer Engineering majors. For more information on its applications, consult further reading below. This book provides further insight into RC circuits in general, both in steady state and non-steady state.

	~~'''Turner, Rufus (1976), RC Circuits 1st edition, H. W. Sams, Oxford Press'''~~

	==External links==		==External links==