Parallel Circuits vs. Series Circuits* - Revision history

Ivan Peshev: Added a new section about delta-Y circuits which was not present before. This method is an application to simplify more complex structures of resistor networks and find equivalent networks through mathematical formulas and calculations. All images are copyright-free and taken as screenshots from an online circuit simulator.

2023-04-17T01:24:53Z

Added a new section about delta-Y circuits which was not present before. This method is an application to simplify more complex structures of resistor networks and find equivalent networks through mathematical formulas and calculations. All images are copyright-free and taken as screenshots from an online circuit simulator.

@@ Line 1: / Line 1: @@
 '''Claimed by Christina Zhao Fall 2018'''
 ==The Main Idea==
 A typical circuit consists of a power source, usually a battery, and electrical elements such as resistors and capacitors. Resistors include light bulbs and do not provide power. Resistors, depending on how they are positioned in a circuit, reduces the voltage or the current that passes through them, and can change the equivalent, or total resistance in a circuit.
@@ Line 177: / Line 180: @@
 == See also ==
 ===Further reading and external links===

Sydney: /* Examples */

2019-12-18T19:57:07Z

Examples

← Older revision		Revision as of 15:57, 18 December 2019
Line 163:		Line 163:

	<math>I_{1}= I_{2} + I_{3}= {\frac{102}{63}}+ {\frac{24}{63}}= {\frac{126}{63}}</math>		<math>I_{1}= I_{2} + I_{3}= {\frac{102}{63}}+ {\frac{24}{63}}= {\frac{126}{63}}</math>


	==Connectedness==		==Connectedness==

Sydney: /* Middling */

2019-11-22T18:17:10Z

Middling

@@ Line 117: / Line 117: @@
 #simple combination of one in-series component or one in-parallel component:
 [[File:Middle_combination.png|frameless|upright=0.7]][http://physicsbook.gatech.edu/File:Middle_combination.PNG]
 [[File:1MiddleQuestion.jpg]]

Sydney: /* Simple */

2019-11-22T17:49:36Z

Simple

← Older revision		Revision as of 13:49, 22 November 2019
Line 91:		Line 91:
	#Purely in-parallel:		#Purely in-parallel:

	[[File:Purely_in_parallel.png\|~~250px~~]]		[[File:Purely_in_parallel.png\|220px]]

	'''Solution'''		'''Solution'''

Sydney: /* Simple */

2019-11-22T17:48:33Z

Simple

← Older revision		Revision as of 13:48, 22 November 2019
Line 71:		Line 71:

	#Purely in-series:		#Purely in-series:
	[[File:Purely_in_series.png\|frameless\|upright=0.4\|250px]~~][http://physicsbook.gatech.edu/File:Purely_in_series.png~~]		[[File:Purely_in_series.png\|frameless\|upright=0.4\|250px]]

	'''Solution'''		'''Solution'''

	Using the loop rule, we know that: ~~<math> \Delta V = 0 </math>~~		Using the loop rule, we know that:

	~~and~~ <math> 0 = \varepsilon - I R_{1} - I R_{2}</math>		<math> \Delta V = 0 </math>

			<math> 0 = \varepsilon - I R_{1} - I R_{2}</math>

	<math> 0= 6 - I (4) - I (12)</math>		<math> 0= 6 - I (4) - I (12)</math>
Line 89:		Line 91:
	#Purely in-parallel:		#Purely in-parallel:

	[[File:Purely_in_parallel.png\|250px]~~][http://physicsbook.gatech.edu/File:Purely_in_parallel.png~~]		[[File:Purely_in_parallel.png\|250px]]

	'''Solution'''		'''Solution'''

Sydney: /* Simple */

2019-11-21T15:52:40Z

Simple

← Older revision		Revision as of 11:52, 21 November 2019
Line 67:		Line 67:

	===Simple===		===Simple===

			'''Question'''

	#Purely in-series:		#Purely in-series:
	[[File:Purely_in_series.png\|frameless\|upright=0.4]][http://physicsbook.gatech.edu/File:Purely_in_series.png]		[[File:Purely_in_series.png\|frameless\|upright=0.4\|250px]][http://physicsbook.gatech.edu/File:Purely_in_series.png]

	~~Answer~~		'''Solution'''

	~~Loop Rule~~: <math> \Delta V = 0 </math>		Using the loop rule, we know that: <math> \Delta V = 0 </math>

	<math> 0 = \varepsilon - I R_{1} - I R_{2}</math>		and <math> 0 = \varepsilon - I R_{1} - I R_{2}</math>

	<math> 0= 6 - I (4) - I (12)</math>		<math> 0= 6 - I (4) - I (12)</math>
Line 83:		Line 85:
	<math> I= .375 A </math>		<math> I= .375 A </math>

			'''Question'''

	#Purely in-parallel:		#Purely in-parallel:

	[[File:Purely_in_parallel.png\|~~200px~~][http://physicsbook.gatech.edu/File:Purely_in_parallel.png]		[[File:Purely_in_parallel.png\|250px]][http://physicsbook.gatech.edu/File:Purely_in_parallel.png]

			'''Solution'''

	Loop Rule: <math> \Delta V = 0 </math>		Loop Rule: <math> \Delta V = 0 </math>
Line 105:		Line 110:
	<math> 6= I 3 </math>		<math> 6= I 3 </math>

	<math> I=2 </math>		<math> I=2 </math>


	===Middling===		===Middling===

Sydney: /* A Computational Model */

2019-11-21T15:49:11Z

A Computational Model

← Older revision		Revision as of 11:49, 21 November 2019
Line 39:		Line 39:

	===A Computational Model===		===A Computational Model===

	~~A schematic is the easiest way to visualize a circuit, and it is helpful for dividing the circuit into solvable sections.~~

	~~The following image shows a real-world example.~~

	~~[[File:paralleldiagram.jpeg]]~~

	~~Each lightbulb acts like a resistor in the previous circuit schematic.~~

	~~This [https://www.physicsclassroom.com/Physics-Interactives/Electric-Circuits/Circuit-Builder/Circuit-Builder-Interactive website] is a simple circuit builder that can be used to simulate circuits.~~

	[[File:Parallel circuit2.png\|500px]]		[[File:Parallel circuit2.png\|500px]]

	This [https://www.circuitlab.com/circuit/g2qzxs/resistors-in-series-and-parallel/ website] is a ~~more complicated circuit~~ builder that can ~~also~~ be used to model circuits and test ~~the~~ differences in current, voltage, and resistance with with various ~~setups.~~		This [https://www.circuitlab.com/circuit/g2qzxs/resistors-in-series-and-parallel/ website] is a schematic builder that can be used to model circuits and test differences in current, voltage, and resistance with with various combinations of parallel and series.

	~~[[File:Parallel circuit1.png\|350px]]~~

	~~'''How do I remember this?'''~~

	~~In order to tell the difference between~~ parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.


	'''Parallel Circuit'''		'''Parallel Circuit'''
Line 67:		Line 50:
	http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm		http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm

	This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in parallel. You will notice that both of the bulbs are bright because the same voltage is going across each of them. Brightness is proportional to voltage, a higher voltage produces a brighter light. In this circuit the lightbulbs are equivalent to ~~a resistor~~. They have current running through them equal to half the total current and all of the voltage the battery puts out.		This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in parallel. You will notice that both of the bulbs are bright because the same voltage is going across each of them. Brightness is proportional to voltage, a higher voltage produces a brighter light. In this circuit, the lightbulbs are equivalent to resistors. They have current running through them equal to half the total current and all of the voltage the battery puts out.

	'''Series Circuit'''		'''Series Circuit'''
Line 75:		Line 58:
	http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm		http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm

	This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in series. You will notice that both of the bulbs are dim because half of the total voltage is going across each of them.Brightness is proportional to voltage, a higher voltage produces a brighter light. So, the brightness of the first example can not be achieved by this second circuit. In this circuit the lightbulbs are equivalent to a resistor. They have the same amount of current running through each of them.		This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in series. You will notice that both of the bulbs are dim because half of the total voltage is going across each of them. Brightness is proportional to voltage, a higher voltage produces a brighter light. So, the brightness of the first example can not be achieved by this second circuit. In this circuit the lightbulbs are equivalent to a resistor. They have the same amount of current running through each of them.

			'''How do I remember this?'''

			In order to tell the difference between parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.

	==Examples==		==Examples==

Sydney: /* A visual Example */

2019-11-21T15:27:16Z

A visual Example

← Older revision		Revision as of 11:27, 21 November 2019
Line 60:		Line 60:
	In order to tell the difference between parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.		In order to tell the difference between parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.

	~~==A visual Example==~~
	'''Parallel Circuit'''		'''Parallel Circuit'''

Line 67:		Line 67:
	http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm		http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm

	This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in parallel. You will notice that both of the bulbs are bright because the same voltage is going across each of them.Brightness is proportional to voltage, a higher voltage produces a brighter light. In this circuit the lightbulbs are equivalent to a resistor. They have current running through them equal to half the total current and all of the voltage the battery puts out.		This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in parallel. You will notice that both of the bulbs are bright because the same voltage is going across each of them. Brightness is proportional to voltage, a higher voltage produces a brighter light. In this circuit the lightbulbs are equivalent to a resistor. They have current running through them equal to half the total current and all of the voltage the battery puts out.

	'''Series Circuit'''		'''Series Circuit'''
Line 75:		Line 75:
	http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm		http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/components_circuits_association-series_parallel.htm

	This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in series. You will notice that both of the bulbs are dim because half of the total voltage is going across each of them.Brightness is proportional to voltage, a higher voltage produces a brighter light. So, the brightness of the first example can not be ~~acheived~~ by this second circuit. In this circuit the lightbulbs are equivalent to a resistor. They have the same amount of current running through each of them.		This shows an example of a simple circuit consisting of a battery and two lightbulbs wired in series. You will notice that both of the bulbs are dim because half of the total voltage is going across each of them.Brightness is proportional to voltage, a higher voltage produces a brighter light. So, the brightness of the first example can not be achieved by this second circuit. In this circuit the lightbulbs are equivalent to a resistor. They have the same amount of current running through each of them.

	==Examples==		==Examples==

Sydney: /* How do I remember this? */

2019-11-21T15:22:50Z

How do I remember this?

← Older revision		Revision as of 11:22, 21 November 2019
Line 56:		Line 56:
	[[File:Parallel circuit1.png\|350px]]		[[File:Parallel circuit1.png\|350px]]

	==How do I remember this?==		'''How do I remember this?'''

	In order to tell the difference between parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.		In order to tell the difference between parallel and series circuits, I like to think of current as being equivalent to water running through pipes. In a straight line, the same amount of water passes through every part of the pipe. Current behaves the same way. So in series circuit the same current runs through all pieces. However, the parallel circuit is equivalent to a pipe with branches. These branches lead to the current being proportionally split by the size of the branch, just like a circuit in parallel.

Sydney: /* The Main Idea */

2019-11-21T15:18:29Z

The Main Idea

← Older revision		Revision as of 11:18, 21 November 2019
Line 6:		Line 6:
	If these resistors are light bulbs, they are connected in line with the battery. The relative brightness decreases across each bulb, making series connections not ideal for something such as house wiring. This drop is consistent with the loop rule, which states that around a full loop of a circuit, the potential difference is 0.		If these resistors are light bulbs, they are connected in line with the battery. The relative brightness decreases across each bulb, making series connections not ideal for something such as house wiring. This drop is consistent with the loop rule, which states that around a full loop of a circuit, the potential difference is 0.

	[~~http://physicsbook.gatech.edu/~~File:Example_series.PNG ~~Example Series~~]		[[File:Example_series.PNG]]

	Resistors connected in parallel are connected to a power source but are on different branches of wire, meaning that the resistors experience the same potential difference. But, due to being connected to different nodes of the circuit, have different currents flowing across them. The branches of a basic parallel circuit looks like rungs of a ladder.		Resistors connected in parallel are connected to a power source but are on different branches of wire, meaning that the resistors experience the same potential difference. But, due to being connected to different nodes of the circuit, have different currents flowing across them. The branches of a basic parallel circuit looks like rungs of a ladder.
	If these resistors are light bulbs, they are connected from a common point to the potential of the battery and all have the same brightness.		If these resistors are light bulbs, they are connected from a common point to the potential of the battery and all have the same brightness.

	[~~http://physicsbook.gatech.edu/~~File:Example_parallel.PNG ~~Example Parallel~~]		[[File:Example_parallel.PNG]]


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

	An ohmic circuit is a set of resistors linked together in an unique combination. It can also ~~includes~~ components such as bulbs, heaters, and meters as long as they can be considered ohmic. As is expected, if all the components obey Ohm's Law V=IR, then it is considered ohmic. Such a circuit is easy to analyze when components are connected in parallel or in series by using Ohm's law. We may need to use other laws when analyzing non-ohmic circuits. Any resistors may become non-ohmic under very high voltage, and some may be so under low voltage.		An ohmic circuit is a set of resistors linked together in an unique combination. It can also include components such as bulbs, heaters, and meters as long as they can be considered ohmic. As is expected, if all the components obey Ohm's Law V=IR, then it is considered ohmic. Such a circuit is easy to analyze when components are connected in parallel or in series by using Ohm's law. We may need to use other laws when analyzing non-ohmic circuits. Any resistors may become non-ohmic under very high voltage, and some may be so under low voltage.

	~~===A Computational Model===~~

	For a purely in-series circuit, (or purely in-series combination of resistors)		For a purely in-series circuit, (or purely in-series combination of resistors)
Line 38:		Line 36:
	<math>{\frac{1}{R}_{total}} = {\frac{1}{R}_{1}} +{\frac{1}{R}_{2}} + {\frac{1}{R}_{3}} + ... + {\frac{1}{R}_{n}}</math>		<math>{\frac{1}{R}_{total}} = {\frac{1}{R}_{1}} +{\frac{1}{R}_{2}} + {\frac{1}{R}_{3}} + ... + {\frac{1}{R}_{n}}</math>

	~~For ohmic~~ circuits,		When a circuit is analyzed, cut up circuits into purely in-series combination of components or purely in-parallel combination of components, calculate resistance of each combination of components. Reduce the circuit until it is purely in-series or in-parallel and calculate the current, total resistance and potential difference between two ends of each component.

	~~When~~ a circuit is ~~analyzed, cut up circuits~~ into ~~purely~~ in-~~series combination of components or purely in~~-~~parallel combination of components, calculate resistance of each combination of components~~. ~~Reduce the~~ circuit ~~until it is purely~~ in-series ~~or in~~-parallel and ~~calculate~~ the current, ~~total~~ resistance ~~and potential difference between two ends of each component~~.		===A Computational Model===

			A schematic is the easiest way to visualize a circuit, and it is helpful for dividing the circuit into solvable sections.

			The following image shows a real-world example.

			[[File:paralleldiagram.jpeg]]

			Each lightbulb acts like a resistor in the previous circuit schematic.

			This [https://www.physicsclassroom.com/Physics-Interactives/Electric-Circuits/Circuit-Builder/Circuit-Builder-Interactive website] is a simple circuit builder that can be used to simulate circuits.

			[[File:Parallel circuit2.png\|500px]]

			This [https://www.circuitlab.com/circuit/g2qzxs/resistors-in-series-and-parallel/ website] is a more complicated circuit builder that can also be used to model circuits and test the differences in current, voltage, and resistance with with various setups.

			[[File:Parallel circuit1.png\|350px]]

	==How do I remember this?==		==How do I remember this?==