Kirchoff's Laws - Revision history

Ehardin30: Added more to the history section, was more descriptive in some of the solutions for practice problems. Guys pls give me full credit <3

2024-04-15T03:56:14Z

Added more to the history section, was more descriptive in some of the solutions for practice problems. Guys pls give me full credit <3

← Older revision		Revision as of 23:56, 14 April 2024
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	Edits: <b>Emma Hardin, Spring 2024</b>		Edits: <b>Emma Hardin, Spring 2024</b>

	[[File:~~Junction~~.~~gif~~\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.		[[File:NewJunction.png\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.
	I<sub>1</sub> + I<sub>4</sub> = I<sub>2</sub> + I<sub>3</sub> + I<sub>5</sub>]]		I<sub>1</sub> + I<sub>4</sub> = I<sub>2</sub> + I<sub>3</sub> + I<sub>5</sub>]]

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	After finding the loop equations you can use a matrix calculator as well to further simplify your task!: [http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref Online Matrix Row Reduction Calculator]		After finding the loop equations you can use a matrix calculator as well to further simplify your task!: [http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref Online Matrix Row Reduction Calculator]

			You can alternatively use a system of equations to find currents, resistance, or capacitors (for when you don't know linear algebra or do not have a calculator present

	An example of how you would format the matrix of a Kirchhoff's law problem is shown below:		An example of how you would format the matrix of a Kirchhoff's law problem is shown below:
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	'''Solution'''		'''Solution'''

	First, write loop rule equations for each of the possible loops in the circuit. There are 3 loop equations that are possible.		First, write loop rule equations for each of the possible loops in the circuit. It is advised, if given a paper version/one that can be edited, to draw the different nodes and loops on the image itself. This helps prevent careless errors. There are 3 loop equations that are possible.

	<math> emf - {I}_{1}{R}_{1} - {I}_{2}{R}_{2} = 0 </math>		<math> emf - {I}_{1}{R}_{1} - {I}_{2}{R}_{2} = 0 </math>
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	[[File:KirchoffLoopRule.jpg\|thumb\|Gustav Kirchhoff]]		[[File:KirchoffLoopRule.jpg\|thumb\|Gustav Kirchhoff]]

	Gustav Kirchhoff was a German physicist who ~~lived during~~ the ~~19th century~~. There are many equations and laws named after him that he helped to discover. His circuit laws (the node rule and loop rule) were the first laws that he conceived, and discovered this during his time as a student at Albertus University of Königsberg in 1845; he later wrote his doctoral dissertation on these laws. Kirchoff went on to explore the topics of spectroscopy and black body radiation after his graduation from Albertus. In addition to his circuit laws, he is also known for his law of thermochemistry and three laws of spectroscopy, the latter of which helped lead to quantum mechanics.		Gustav Kirchhoff (1824-1887) was a German physicist who is credited for the theory of spectrum analysis and Kirchoff's Laws (1845) among other accolades. There are many equations and laws named after him that he helped to discover. His circuit laws (the node rule and loop rule) were the first laws that he conceived, and discovered this during his time as a student at Albertus University of Königsberg in 1845; he later wrote his doctoral dissertation on these laws. Kirchoff went on to explore the topics of spectroscopy and black body radiation after his graduation from Albertus at the University of Berlin (when he became a lecturer, professor, and eventually chair of mathematical physics). In addition to his circuit laws, he is also known for his law of thermochemistry, determining the composition of the Sun, and the three laws of spectroscopy, the latter of which helped lead to quantum mechanics.

	== See Also ==		== See Also ==
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	* http://higheredbcs.wiley.com/legacy/college/cutnell/0470223553/concept_sims/sim34/sim34.html		* http://higheredbcs.wiley.com/legacy/college/cutnell/0470223553/concept_sims/sim34/sim34.html
	* http://www.falstad.com/circuit/		* http://www.falstad.com/circuit/
			* https://www.britannica.com/biography/Gustav-Robert-Kirchhoff
	* Schuster, D. (Producer). (2013). Kirchhoff's Loop and Junction Rules Theory [Motion picture]. United States of America: YouTube.		* Schuster, D. (Producer). (2013). Kirchhoff's Loop and Junction Rules Theory [Motion picture]. United States of America: YouTube.
	* Schuster, D. (Producer). (2013). Kirchhoff's Rules (Laws) Worked Example [Motion picture]. United States of America: YouTube.		* Schuster, D. (Producer). (2013). Kirchhoff's Rules (Laws) Worked Example [Motion picture]. United States of America: YouTube.

Ehardin30 at 03:30, 15 April 2024

2024-04-15T03:30:09Z

← Older revision		Revision as of 23:30, 14 April 2024
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	Edits: <b>~~Regina Ivanna Gomez Quiroz~~, Spring ~~2023~~</b>		Edits: <b>Emma Hardin, Spring 2024</b>

	[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.		[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.

Daniel72: /* The Main Idea */ While the equation for Loop 2 was mathematically consistent, flipping the signs (which is equivalent mathematically) aligns more with the explanation given by the paragraph below the three loop equations.

2023-11-11T16:35:50Z

The Main Idea: While the equation for Loop 2 was mathematically consistent, flipping the signs (which is equivalent mathematically) aligns more with the explanation given by the paragraph below the three loop equations.

← Older revision		Revision as of 12:35, 11 November 2023
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	LOOP 1: <math> \Delta {V}_1 = emf - I_1R_1 = 0 </math>		LOOP 1: <math> \Delta {V}_1 = emf - I_1R_1 = 0 </math>

	LOOP 2: <math> \Delta {V}_2 = -~~I_1R_1 +~~ I_2R_2 = 0 </math>		LOOP 2: <math> \Delta {V}_2 = I_1R_1 - I_2R_2 = 0 </math>

	LOOP 3: <math> \Delta {V}_3 = emf - I_2R_2 = 0 </math>		LOOP 3: <math> \Delta {V}_3 = emf - I_2R_2 = 0 </math>
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	[[File: Screenshot_2021-11-28_at_21-56-49_GlowScript_IDE.png ‎]]		[[File: Screenshot_2021-11-28_at_21-56-49_GlowScript_IDE.png ‎]]




	==Examples==		==Examples==

Daniel72: Swapped the order of how the first law is introduced to make it consistent with how the second law is introduced.

2023-11-11T16:17:32Z

Swapped the order of how the first law is introduced to make it consistent with how the second law is introduced.

← Older revision		Revision as of 12:17, 11 November 2023
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	<b>Kirchoff's Laws</b> are two fundamental principles of electric circuits and are used to determine the behaviors of electric circuits and their components. They serve as a guide for how circuits will behave and are accurate for all DC and low-frequency AC circuits. These principles are used to measure voltage and current in [http://www.physicsbook.gatech.edu/Ammeters,Voltmeters,Ohmmeters voltmeters and ammeters].		<b>Kirchoff's Laws</b> are two fundamental principles of electric circuits and are used to determine the behaviors of electric circuits and their components. They serve as a guide for how circuits will behave and are accurate for all DC and low-frequency AC circuits. These principles are used to measure voltage and current in [http://www.physicsbook.gatech.edu/Ammeters,Voltmeters,Ohmmeters voltmeters and ammeters].

	<b>Kirchoff's ~~Node Rule~~</b>, also known as <b>Kirchoff's ~~First Law~~</b> or <b>Kirchoff's Junction Rule</b>, further exercises the law of Conservation of Charge and states that if current is constant, all the current that flows through one junction must be equal to all the current that flows out of the junction. This rule can be applied both to [[Electron and Conventional Current\|conventional]] and [[Electron and Conventional Current\|electron currents]]. This rule is not a fundamental principle, but rather a consequence of the fundamental principle of conservation of charge and the definition of steady-state. This law essentially states that the net amount of current entering a particular juncture in the system is equal to the net amount of current leaving the system. A mathematical way to think about is that the sum of the currents entering a point will be equal to the sum leaving it.		<b>Kirchoff's First Law</b>, also known as <b>Kirchoff's Node Rule</b> or <b>Kirchoff's Junction Rule</b>, further exercises the law of Conservation of Charge and states that if current is constant, all the current that flows through one junction must be equal to all the current that flows out of the junction. This rule can be applied both to [[Electron and Conventional Current\|conventional]] and [[Electron and Conventional Current\|electron currents]]. This rule is not a fundamental principle, but rather a consequence of the fundamental principle of conservation of charge and the definition of steady-state. This law essentially states that the net amount of current entering a particular juncture in the system is equal to the net amount of current leaving the system. A mathematical way to think about is that the sum of the currents entering a point will be equal to the sum leaving it.

	[[File:Visual_Model2.png\|thumb\|The Loop rule states that the sum of voltage around a loop is equal to 0.		[[File:Visual_Model2.png\|thumb\|The Loop rule states that the sum of voltage around a loop is equal to 0.

Rquiroz7: Added applications section

2023-04-17T03:59:15Z

Added applications section

← Older revision		Revision as of 23:59, 16 April 2023
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	Edits: <b>~~Archie Chaudhury Fall 2021~~</b>		Edits: <b>Regina Ivanna Gomez Quiroz, Spring 2023</b>

	[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.		[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.
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	Linear algebra is also intertwined with Kirchhoff's laws involving loops and nodes as complex and large circuits with many components can often lead to many different loops and the amount of loop and node equations can often get out of hand very quickly. As a result, we can use matrices to simplify the algebra involved with solving for currents in components that are a part of large circuits with many different loop and node equations. After creating the matrix we need skills from linear algebra in order to find the row reduced form of the augmented matrix that we create. With this reduced version of the matrix, we can find the current or resistances of the different parts of the circuit in a much easier and more timely fashion.		Linear algebra is also intertwined with Kirchhoff's laws involving loops and nodes as complex and large circuits with many components can often lead to many different loops and the amount of loop and node equations can often get out of hand very quickly. As a result, we can use matrices to simplify the algebra involved with solving for currents in components that are a part of large circuits with many different loop and node equations. After creating the matrix we need skills from linear algebra in order to find the row reduced form of the augmented matrix that we create. With this reduced version of the matrix, we can find the current or resistances of the different parts of the circuit in a much easier and more timely fashion.

			==Applications==

			===Circuit Design ===
			Kirchhoff's Laws are vital when designing electrical circuits as well as when we are analyzing them. The circuits that these laws can help us design and analyze can range from those found in our household appliances to more complex ones used in industrial applications at a large scale. In engineering, these laws are relevant because they help us design circuits that meet specific performance requirements.

			===Current Measurement===
			Kirchhoff's Laws can be used to measure the current flowing at various specific points of a circuit. By applying these laws at specific locations in a circuit, it can help us determine the amount of current entering and leaving that location or node. This aids us when we want to measure and control the flow of current in a circuit while designing or analyzing said circuit.

			===Voltage Measurement===
			Kirchhoff's Laws can be used to measure the voltage at different points of a circuit. By applying these laws to a loop in a circuit, it can help us determine the amount of voltage across all the points in that loop. This aids us when we want to measure and control the voltage levels in a circuit while designing or analyzing said circuit.

	==History==		==History==

Achaudhury9 at 02:59, 29 November 2021

2021-11-29T02:59:00Z

← Older revision		Revision as of 22:59, 28 November 2021
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	Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here]. The result is shown below:		Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here]. The result is shown below:

			[[File: Screenshot_2021-11-28_at_21-56-49_GlowScript_IDE.png ‎]]

Achaudhury9 at 02:57, 29 November 2021

2021-11-29T02:57:07Z

← Older revision		Revision as of 22:57, 28 November 2021
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	Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here]. The result is shown below:		Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here]. The result is shown below:

	~~<iframe src="https://trinket.io/embed/glowscript/9f76be45ce" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~

Achaudhury9 at 02:47, 29 November 2021

2021-11-29T02:47:26Z

← Older revision		Revision as of 22:47, 28 November 2021
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	Click here for a computational model of an [http://www.falstad.com/circuit/ online circuit simulator]. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. The voltage is always conserved, as long as the node rule can apply.		Click here for a computational model of an [http://www.falstad.com/circuit/ online circuit simulator]. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. The voltage is always conserved, as long as the node rule can apply.

	Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here].		Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here]. The result is shown below:

			<iframe src="https://trinket.io/embed/glowscript/9f76be45ce" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>


	==Examples==		==Examples==

Achaudhury9 at 02:41, 29 November 2021

2021-11-29T02:41:58Z

← Older revision		Revision as of 22:41, 28 November 2021
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	Edits: ~~Heeva Taghian Fall 2019~~		Edits: <b>Archie Chaudhury Fall 2021</b>
	Archie Chaudhury Fall 2021

	[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.		[[File:Junction.gif\|thumb\|The node (or junction) rule states that the current flowing in is equal to the current that flows out.

Achaudhury9 at 02:41, 29 November 2021

2021-11-29T02:41:13Z

← Older revision		Revision as of 22:41, 28 November 2021
Line 152:		Line 152:
	Click here for a computational model of an [http://www.falstad.com/circuit/ online circuit simulator]. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. The voltage is always conserved, as long as the node rule can apply.		Click here for a computational model of an [http://www.falstad.com/circuit/ online circuit simulator]. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. The voltage is always conserved, as long as the node rule can apply.

	Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action.		Another computational model, taken from an open source article [https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/ is given here]. This depicts the loop rule in a RC circuit with a bulb. It depicts how the net voltage in the bulb tends to zero over time, thus signifying a physical example of the loop rule in action. The Glowscript code can be found [https://www.glowscript.org/#/user/achaudhury9/folder/MyPrograms/program/LoopRuleRC here].

	==Examples==		==Examples==