Current in an LC Circuit: Difference between revisions

Revision as of 23:10, 5 December 2015

CLAIMED BY: Kelsey Dobson 12/5/2015

An LC circuit contains an inductor and a capacitor, and because of the inductor's sluggishness and resistance to change the current, the charge in this circuit can oscillate back and forth forever.

The Main Idea

A circuit containing an inductor "L" and a capacitor "C" is called an LC circuit. This circuit can oscillate continuously if the resistance is small. Accordingly, the connecting wires in an LC circuit are low-resistance thick copper wires. Here is the basic idea behind the process of an LC circuit:

A capacitor is charged initially, and then a switch is closed. This connects the capacitor to the inductor. At first, because of the nature of an inductor, it is difficult for charge on the capacitor to flow through the inductor. This is because the inductor opposes all attempts to change the current. However, since an inductor cannot completely prevent a current from changing, there is more current little by little. This drains the capacitor of its charge.

At the moment the capacitor runs out of charge, there is a current in the inductor, and because inductors are sluggish by nature, the current can't immediately change to zero. Therefore, the system does not come to equililbrium and instead increases the charge in the capacitor. When the capacitor is fully charged, it starts to discharge back through the inductor, and the process repeats. Since the circuit will never reach equilibrium and current never reaches zero, this oscillating process repeats forever. Oscillations could reach a stopping point if there is some resistance, but it may still go through multiple cycles before equilibrium is reached.

A Mathematical Model

An LC circuit has an energy conservation rule associated with it. The energy conservation loop rule for an LC circuit is: [math]\displaystyle{ \delta\V_{capacitor} + \delta\V_{inductor} = \frac{1}{C}-L\frac{dI}{dt} = 0 }[/math]

A Computational Model

Examples

Simple

Emf of an entire solenoid:

B=μ0NI/d emf = |d(mag flux)/dt| = d/dt|μ0NI/d(piR^2)| = μ0NI/d(piR^2)dI/dt emf = N(μ0N/d(piR^2)dI/dt)= (μ0N^2/d(piR^2)dI/dt)

Middling

What is the self inductance of a common solenoid?

-The self inductance is the constant in the inductance formula solved above. This means that the self inductance constant for a solenoid is (μ0N/d(piR^2)

Difficult

What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.

- the self inductance would be (μ0100/1(pi.01^2)= 3.95e-8 henries

Connectedness

This topic is interesting because solenoids are a very common placed tool. It is important to know how they operate in order to use them to the best of their capabilities.
This topic is personally connected to me because of my major. I am a mechanical engineer and am currently enrolled in ME2110, the "robot building class". In this class to assist with our designs, we often used solenoids as deployment mechanism. Being able to learn about this topic while working with the objects hands on in a non-physics environment helped me immensely in my design process and physics career.

History

The history of inductance goes back quite a long time ago and is pretty complicated. In the early 19th century there were actually two scientist discovering inductance in parallel with each other, one in America and one in England. These two scientist names are Joseph Henry and Michael Faraday. Because of this there is no one named founder of inductance, but both of them did receive credit. Inductance now finds itself as one of Faraday's Laws, giving Michael Faraday his due credit. While the units for inductance are "Henries" named after Joseph Henry.

@@ Line 2: / Line 2: @@
 /5/2015
-Short Description of Topic
+An LC circuit contains an inductor and a capacitor, and because of the inductor's sluggishness and resistance to change the current, the charge in this circuit can oscillate back and forth forever.
-Contents [hide]
+==The Main Idea==
-The Main Idea
-.1 A Mathematical Model
-.2 A Computational Model
-Examples
-.1 Simple
-.2 Middling
-.3 Difficult
-Connectedness
-History
-See also
-.1 Further reading
-.2 External links
-References
-The Main Idea[edit]
-State, in your own words, the main idea for this topic
+A circuit containing an inductor "L" and a capacitor "C" is called an LC circuit. This circuit can oscillate continuously if the resistance is small. Accordingly, the connecting wires in an LC circuit are low-resistance thick copper wires. Here is the basic idea behind the process of an LC circuit:
-A Mathematical Model[edit]
+A capacitor is charged initially, and then a switch is closed. This connects the capacitor to the inductor. At first, because of the nature of an inductor, it is difficult for charge on the capacitor to flow through the inductor. This is because the inductor opposes all attempts to change the current. However, since an inductor cannot completely prevent a current from changing, there is more current little by little. This drains the capacitor of its charge.
-What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.
-A Computational Model[edit]
+At the moment the capacitor runs out of charge, there is a current in the inductor, and because inductors are sluggish by nature, the current can't immediately change to zero. Therefore, the system does not come to equililbrium and instead increases the charge in the capacitor. When the capacitor is fully charged, it starts to discharge back through the inductor, and the process repeats. Since the circuit will never reach equilibrium and current never reaches zero, this oscillating process repeats forever. Oscillations could reach a stopping point if there is some resistance, but it may still go through multiple cycles before equilibrium is reached.
-How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
-Examples[edit]
+===A Mathematical Model===
-Be sure to show all steps in your solution and include diagrams whenever possible
-Simple[edit]
+An LC circuit has an energy conservation rule associated with it. The energy conservation loop rule for an LC circuit is:
-Middling[edit]
+<math> \delta\V_{capacitor} + \delta\V_{inductor} = \frac{1}{C}-L\frac{dI}{dt} = 0 </math>
-Difficult[edit]
-Connectedness[edit]
-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?
-History[edit]
-Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
-See also[edit]
+===A Computational Model===
-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[edit]
-Books, Articles or other print media on this topic
-External links[edit]
-[1]
+==Examples==
+===Simple===
+Emf of an entire solenoid:
+B=μ0NI/d
+emf = |d(mag flux)/dt| = d/dt|μ0NI/d(piR^2)| = μ0NI/d(piR^2)dI/dt
+emf = N(μ0N/d(piR^2)dI/dt)= (μ0N^2/d(piR^2)dI/dt)
+===Middling===
+What is the self inductance of a common solenoid?
+-The self inductance is the constant in the inductance formula solved above. This means that the self inductance constant for a solenoid is (μ0N/d(piR^2)
+===Difficult===
+What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.
+- the self inductance would be (μ0100/1(pi.01^2)= 3.95e-8 henries
+==Connectedness==
+#This topic is interesting because solenoids are a very common placed tool. It is important to know how they operate in order to use them to the best of their capabilities.
+#This topic is personally connected to me because of my major. I am a mechanical engineer and am currently enrolled in ME2110, the "robot building class". In this class to assist with our designs, we often used solenoids as deployment mechanism. Being able to learn about this topic while working with the objects hands on in a non-physics environment helped me immensely in my design process and physics career.
+==History==
+The history of inductance goes back quite a long time ago and is pretty complicated. In the early 19th century there were actually two scientist discovering inductance in parallel with each other, one in America and one in England. These two scientist names are Joseph Henry and Michael Faraday. Because of this there is no one named founder of inductance, but both of them did receive credit. Inductance now finds itself as one of Faraday's Laws, giving Michael Faraday his due credit. While the units for inductance are "Henries" named after Joseph Henry.
+== See also ==
+Faraday's Law
+===Further reading===
+Information for this page was found in Matter and Interactions Volume II. If you would like to know more about this topic or other topics like it, please reference this book.
+===External links===
+Images were found at http://www.calctool.org/CALC/phys/electromagnetism/solenoid
+==References==
-References[edit]
 This section contains the the references you used while writing this page
+[[Category:Which Category did you place this in?]]

Current in an LC Circuit: Difference between revisions

Revision as of 23:10, 5 December 2015

The Main Idea

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See also

Further reading

External links

References

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