Problem Solving - Revision history

Monicahanon: /* Kirchhoff's Current Law */

2017-11-30T04:28:50Z

Kirchhoff's Current Law

← Older revision		Revision as of 00:28, 30 November 2017
Line 27:		Line 27:
	===Kirchhoff's Current Law===		===Kirchhoff's Current Law===

	[[File:~~junction2~~.jpeg\|500px\|thumb\|center\|Kirchhoff's Current Law]]		[[File:Junction rule.jpeg\|500px\|thumb\|center\|Kirchhoff's Current Law]]

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T04:28:29Z

← Older revision		Revision as of 00:28, 30 November 2017
Line 27:		Line 27:
	===Kirchhoff's Current Law===		===Kirchhoff's Current Law===

	[[File:junction2.jpeg\|500px\|thumb\|center]]		[[File:junction2.jpeg\|500px\|thumb\|center\|Kirchhoff's Current Law]]

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T04:27:22Z

Kirchhoff's Current Law

← Older revision		Revision as of 00:27, 30 November 2017
Line 27:		Line 27:
	===Kirchhoff's Current Law===		===Kirchhoff's Current Law===

	[[File:junction2.jpeg\|500px\|thumb\|center~~\|Graph representation of a circuit~~]]		[[File:junction2.jpeg\|500px\|thumb\|center]]

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T04:27:04Z

← Older revision		Revision as of 00:27, 30 November 2017
Line 27:		Line 27:
	===Kirchhoff's Current Law===		===Kirchhoff's Current Law===

	[[File:junction2.jpeg]]		[[File:junction2.jpeg\|500px\|thumb\|center\|Graph representation of a circuit]]

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T04:26:31Z

Loop Rule (Kirchhoff's voltage law)

← Older revision		Revision as of 00:26, 30 November 2017
Line 25:		Line 25:
	We know from Ohm's law that <math> V = I * R </math>. Then, in the previous graph for example, we would have that <math> V_{edge1} = I * R = (direction) * R_{1} = 1 * R_{1} </math>.		We know from Ohm's law that <math> V = I * R </math>. Then, in the previous graph for example, we would have that <math> V_{edge1} = I * R = (direction) * R_{1} = 1 * R_{1} </math>.

	~~[[File:junction2.jpeg]]~~===Kirchhoff's Current Law===		===Kirchhoff's Current Law===

			[[File:junction2.jpeg]]

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T04:25:34Z

Kirchhoff's Current Law

← Older revision		Revision as of 00:25, 30 November 2017
Line 25:		Line 25:
	We know from Ohm's law that <math> V = I * R </math>. Then, in the previous graph for example, we would have that <math> V_{edge1} = I * R = (direction) * R_{1} = 1 * R_{1} </math>.		We know from Ohm's law that <math> V = I * R </math>. Then, in the previous graph for example, we would have that <math> V_{edge1} = I * R = (direction) * R_{1} = 1 * R_{1} </math>.

	===Kirchhoff's Current Law===		[[File:junction2.jpeg]]===Kirchhoff's Current Law===

	We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:		We know from Kirchhoff's law that the sum of the currents in each node is zero. This means that the current flowing into the node is the same as the current flowing out of the node. Therefore the multiplication of each column of A by the current vector, y, must be equal to zero:

2017-11-30T03:50:08Z

← Older revision		Revision as of 23:50, 29 November 2017
Line 74:		Line 74:

	[[File:Linear_circut_example6.png\|140px\|thumb\|center]]		[[File:Linear_circut_example6.png\|140px\|thumb\|center]]

	~~==Connectedness==~~
	~~#How is this topic connected to something that you are interested in?~~
	~~#How is it connected to your major?~~
	~~#Is there an interesting industrial application?~~

	== See also ==		== See also ==

2017-11-30T03:49:47Z

← Older revision		Revision as of 23:49, 29 November 2017
Line 81:		Line 81:

	== See also ==		== See also ==

	~~Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?~~

	===Further reading===		===Further reading===

2017-11-30T03:46:16Z

← Older revision		Revision as of 23:46, 29 November 2017
Line 73:		Line 73:
	Finally, we can find the currents using <math>\vec{y} = -CA\vec{x}</math>:		Finally, we can find the currents using <math>\vec{y} = -CA\vec{x}</math>:

	[[File:Linear_circut_example6.png\|~~150px~~\|thumb\|center]]		[[File:Linear_circut_example6.png\|140px\|thumb\|center]]

	==Connectedness==		==Connectedness==

2017-11-30T03:39:59Z

← Older revision		Revision as of 23:39, 29 November 2017
Line 67:		Line 67:
	[[File:Linear_circut_example4.png\|500px\|thumb\|center]]		[[File:Linear_circut_example4.png\|500px\|thumb\|center]]

	Solving for x, we get:		Solving for x, we get the voltages:

	[[File:Linear_circut_example5.png\|150px\|thumb\|center]]		[[File:Linear_circut_example5.png\|150px\|thumb\|center]]

			Finally, we can find the currents using <math>\vec{y} = -CA\vec{x}</math>:

			[[File:Linear_circut_example6.png\|150px\|thumb\|center]]

	==Connectedness==		==Connectedness==