Okaykeeseok: Created page with "claimed by Mchan46 ==Main Idea== :A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another. :The..."

2015-12-03T05:59:30Z

Created page with "claimed by Mchan46 ==Main Idea== :A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another. :The..."

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claimed by [[User:Mchan46|Mchan46]]
==Main Idea==

:A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another.
:The electrical connection is not branched in any way. One can visualize this circuit as simply a closed loop.
:Often times, the simple series circuit may include but are not limited to: a number of resistors, switches, and of course, batteries.
:Keep in mind, if there is an open switch or break in the circuit, no current flows.

===A Mathematical Model===

:Kirchhoff's Current and Voltage Laws apply in a series circuit.
::Through Kirchhoff's Current Law, we know that the sum of all current going in must equal the sum of all current going out.
:::<math>\sum{I}_{in} - \sum{I}_{out} = 0</math>
::Since there are no nodes for the current to split up, the current throughout a series circuit will always be the same through each component.
::Through Kirchhoff's Voltage Law, the sum of all voltage in a closed system must be zero.
:::<math>\sum{V}_{Battery} - \sum{V}_{Components} = 0</math>
<br />
:Ohm's Law is extremely useful in finding the voltages, resistances, and current throughout the series circuit.
::Ohm's Law gives us the following formula:
:::<math>V=IR</math>; it can be rearranged to yield <math>I=\frac{V}{R}</math> and <math>R = \frac{V}{I}</math>
<br />
:Total Resistance in a series circuit is the sum of all resistances. It can be used to find the overall current in the circuit, which can then be used to find individual resistances.
::Total resistance is described by:
:::<math>R_T=\sum_{n=1}^N {R}_{Series}=R_1+R_2+R_3+...R_N</math>

===A Computational Model===

:The best way to visualize a series circuit is to draw a schematic, which is a simplified representation of the circuit in real life.
:Resistors are usually represented in a schematic with [[File:Resistor Symbol.png|100px]]
:Batteries are represented in a schematic by [[File:Schematic-symbols-battery.png|75px]]
:Switches can be open or closed. An open switch is represented by [[File:Schematic-symbols-switch.png|75px]]
==Examples==

For these examples, find the values specified.

===Simple===
Find the current in the circuit.
:[[File:Problem1Series_Circuits.JPG|350px]]

===Middling===
Find the voltage across the battery if the current in the circuit is 0.5 A
:[[File:Problem2Series_Circuits.JPG|350px]]

===Difficult===
The voltage across <math>R_1</math> is 5 volts. The voltage across <math>R_2</math> is 6 volts. What are the resistances of <math>R_1, R_2,</math> and <math>R_3</math> if the current measured across <math>R_3</math> is .65 A and the voltage of the battery is 16V?
:[[File:Problem3Series_Circuits.JPG|350px]]
==Solutions to Examples==
===Simple===
<math>I=0</math> Since the circuit is open, there is no way for current to flow through the circuit.

===Middling===
:1. Find Total Resistance
::<math>R_T=R_1+R_2+R_3=10+35+15=60</math> Ohms
:2. Use Ohm's Law (current is given already)
::<math>V=IR=0.5\bullet60=30</math> Volts

===Difficult===
:1. Note that current across a series circuit is the same.
::Current = 0.65 A
:2. Sum of battery voltage is equal to the sum of all voltage across resistors.
::<math>\sum{V}_{Battery} = \sum{V}_{Components}</math>
::<math>16 = 5 + 6 + V_3</math>
::<math>V_3 = 5</math>
:3. Use the rearranged Ohm's Law to find the resistances.
::<math>R=\frac{V}{I}</math>
::<math>R_1=\frac{5}{.65}=7.69</math> Ohms
::<math>R_2=\frac{6}{.65}=9.23</math> Ohms
::<math>R_3=\frac{5}{.65}=7.69</math> Ohms

==Connectedness==
:Series circuits are the most basic type of circuits.
:They are used in all electronics; even parallel circuits can be simplified into a series circuit!
:Some realistic applications include making lights, motors, and other electrical appliances work.

==History==

:Series circuits date as far back as when the first battery was invented.
:In the 1800's Alessandro Volta invented the first battery; it was originally used to produce hydrogen and oxygen from water.
:Around the 1880's, however, light bulbs were commercialized and used to illuminate cities- none of this could be done without the basic circuit.

== See also ==

:[[Ohm's Law]]
:[[Resistors and Conductivity]]
:[[Current]]
:[[Ammeters,Voltmeters,Ohmmeters]]
:[[Power in a circuit]]
:[[RL Circuit]]
:[[LC Circuit]]

===Further reading===

:Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015)

===External links===

:[http://www.allaboutcircuits.com/ All About Circuits]
:[http://www.build-electronic-circuits.com/ BuildElectronicCircuits]
:[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Electrical Circuits]

==References==
:"All About Circuits - Electrical Engineering & Electronics Community." All About Circuits - Electrical Engineering & Electronics Community. Web. 30 Nov. 2015.
:"Build Electronic Circuits - Electronics Explained in a Simple Way." Build Electronic Circuits. Web. 30 Nov. 2015.
:Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015)
:Soclof, Sidney. HowStuffWorks. HowStuffWorks.com. Web. 30 Nov. 2015.

[[Category:Simple Circuits]]

Series Circuit - Revision history

Okaykeeseok: Created page with "claimed by Mchan46 ==Main Idea== :A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another. :The..."