http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=NteisslerPhysics Book - User contributions [en]2026-04-24T19:46:44ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=20426Transformers (Circuits)2015-12-08T16:32:00Z<p>Nteissler: /* Connectedness */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
:'''1. How is this topic connected to something that you are interested in?'''<br />
<br />
Although Dr. Greco said he found the circuits chapter and material dull, as a Computer Science major with an interest in Electrical Engineering and tinkering with hardware, I thought it was a great practical part of the course. Our textbook ''Electric Potential. In Matter & interactions (4th ed.)'' introduces transformers in the context of induction and Faraday in a more conceptual sense. I believed they should also be shown alongside circuits to demonstrate their practicality. It really helped with my understanding the view the setup and waveform of a circuit involving transformers. <br />
<br />
I even tried to add a bridge rectifier and regulator to the circuit to show the AC being transformed back into DC. My circuits knowledge is somewhat limited and I was unable to properly connect this circuit.<br />
<br />
:'''2. How is it connected to your major?'''<br />
<br />
In today's world of open source hardware and software, it is very important for a Computer Science major to understand circuits beyond a basic level and be able to incorporate circuits and moving parts into their work. With Raspberry Pis, Arduinos, and everything else the internet has to offer, a CS major is severely limiting themselves by not studying topics like theses.<br />
<br />
:'''3. Is there an interesting industrial application?'''<br />
<br />
I think the interesting thing about industrial applications is how transformers appear in such a simple context in many power cords for appliances today. I remember back to my first interaction with one: Years ago at a friend's house we were playing songs on his electrical keyboard. At a point, we decided to move the keyboard and in the process broke the plastic casing off the transformer of the power cord. I was young, so didn't recognize it as a danger or issue at the time. I can vividly remember the copper coils (I think). At any rate, I plugged it in and was touching the coils and got an arm numbing shock. But my shock boils down to just a simple transformer that any Physics 2 student could make and understand.<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=20425Transformers (Circuits)2015-12-08T16:31:19Z<p>Nteissler: /* Connectedness */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
:'''1. How is this topic connected to something that you are interested in?'''<br />
<br />
Although Dr. Greco said he found the circuits chapter and material dull, as a Computer Science major with an interest in Electrical Engineering and tinkering with hardware, I thought it was a great practical part of the course. Our textbook ''Electric Potential. In Matter & interactions (4th ed.)'' introduces transformers in the context of induction and Faraday in a more conceptual sense. I believed they should also be shown alongside circuits to demonstrate their practicality. It really helped with my understanding the view the setup and waveform of a circuit involving transformers. <br />
<br />
I even tried to add a bridge rectifier and regulator to the circuit to show the AC being transformed back into DC. My circuits knowledge is somewhat limited and I was unable to properly connect this circuit.<br />
<br />
:'''2. How is it connected to your major?'''<br />
<br />
In today's world of open source hardware and software, it is very important for a Computer Science major to understand circuits beyond a basic level and be able to incorporate circuits and moving parts into their work. With Raspberry Pis, Arduinos, and everything else the internet has to offer, as CS major is severely limiting themselves by not studying topics like theses.<br />
<br />
:'''3. Is there an interesting industrial application?'''<br />
<br />
I think the interesting thing about industrial applications is how transformers appear in such a simple context in many power cords for appliances today. I remember back to my first interaction with one: Years ago at a friend's house we were playing songs on his electrical keyboard. At a point, we decided to move the keyboard and in the process broke the plastic casing off the transformer of the power cord. I was young, so didn't recognize it as a danger or issue at the time. I can vividly remember the copper coils (I think). At any rate, I plugged it in and was touching the coils and got an arm numbing shock. But my shock boils down to just a simple transformer that any Physics 2 student could make and understand.<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=14518Transformers (Circuits)2015-12-05T18:07:01Z<p>Nteissler: /* Connectedness */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
:'''1. How is this topic connected to something that you are interested in?'''<br />
<br />
Although Dr. Greco said he found the circuits chapter and material dull, as a Computer Science major with an interest in Electrical Engineering and tinkering with hardware, I thought it was a great practical part of the course. Our textbook ''Electric Potential. In Matter & interactions (4th ed.)'' introduces transformers in the context of induction and Faraday in a more conceptual sense. I believed they should also be shown alongside circuits to demonstrate their practicality. It really helped with my understanding the view the setup and waveform of a circuit involving transformers. <br />
<br />
I even tried to add a bridge rectifier and regulator to the circuit to show the AC being transformed back into DC. My circuits knowledge is somewhat limited (although I still believe the limitations might have been on the iCircuit software I was using), and I was unable to properly connect this circuit. <br />
<br />
:'''2. How is it connected to your major?'''<br />
<br />
In today's world of open source hardware and software, it is very important for a Computer Science major to understand circuits beyond a basic level and be able to incorporate circuits and moving parts into their work. With Raspberry Pis, Arduinos, and everything else the internet has to offer, as CS major is severely limiting themselves by not studying topics like theses.<br />
<br />
:'''3. Is there an interesting industrial application?'''<br />
<br />
I think the interesting thing about industrial applications is how transformers appear in such a simple context in many power cords for appliances today. I remember back to my first interaction with one: Years ago at a friend's house we were playing songs on his electrical keyboard. At a point, we decided to move the keyboard and in the process broke the plastic casing off the transformer of the power cord. I was young, so didn't recognize it as a danger or issue at the time. I can vividly remember the copper coils (I think). At any rate, I plugged it in and was touching the coils and got an arm numbing shock. But my shock boils down to just a simple transformer that any Physics 2 student could make and understand.<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=14512Transformers (Circuits)2015-12-05T18:06:03Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
#'''How is this topic connected to something that you are interested in?'''<br />
<br />
Although Dr. Greco said he found the circuits chapter and material dull, as a Computer Science major with an interest in Electrical Engineering and tinkering with hardware, I thought it was a great practical part of the course. Our textbook ''Electric Potential. In Matter & interactions (4th ed.)'' introduces transformers in the context of induction and Faraday in a more conceptual sense. I believed they should also be shown alongside circuits to demonstrate their practicality. It really helped with my understanding the view the setup and waveform of a circuit involving transformers. <br />
<br />
I even tried to add a bridge rectifier and regulator to the circuit to show the AC being transformed back into DC. My circuits knowledge is somewhat limited (although I still believe the limitations might have been on the iCircuit software I was using), and I was unable to properly connect this circuit. <br />
<br />
#'''How is it connected to your major?'''<br />
<br />
In today's world of open source hardware and software, it is very important for a Computer Science major to understand circuits beyond a basic level and be able to incorporate circuits and moving parts into their work. With Raspberry Pis, Arduinos, and everything else the internet has to offer, as CS major is severely limiting themselves by not studying topics like theses.<br />
<br />
#Is there an interesting industrial application?<br />
<br />
I think the interesting thing about industrial applications is how transformers appear in such a simple context in many power cords for appliances today. I remember back to my first interaction with one: Years ago at a friend's house we were playing songs on his electrical keyboard. At a point, we decided to move the keyboard and in the process broke the plastic casing off the transformer of the power cord. I was young, so didn't recognize it as a danger or issue at the time. I can vividly remember the copper coils (I think). At any rate, I plugged it in and was touching the coils and got an arm numbing shock. But my shock boils down to just a simple transformer that any Physics 2 student could make and understand.<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=13464Transformers (Circuits)2015-12-05T04:41:06Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=13463Transformers (Circuits)2015-12-05T04:40:22Z<p>Nteissler: /* Circuit Diagrams */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=13457Transformers (Circuits)2015-12-05T04:39:24Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=13449Transformers (Circuits)2015-12-05T04:37:46Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Below are animated circuit diagrams for a step-up transformer, step-down transformer, and even a somewhat pointless transformer that has a 1:1 voltage ratio. The right side panel lists the properties of the transformer. The primary inductance and coupling coefficient are beyond the scope of my knowledge. However I did enough research to know that the ''Coupling Coefficient'' is some property of a transformer derived from the self inductance of each coil. I believe for most discussions on transformers, the "ideal" coupling coefficient is 100%. The waveform is graphing the voltage of the left loop (blue) and voltage of the right loop (green).<br />
<br />
[[File:step_up.gif|500px|border|frame|center|A step-up transformer that doubles voltage and halves current]]<br />
<br />
[[File:step_down.gif|500px|border|frame|center|A step-down transformer that halves voltage and double current]]<br />
<br />
[[File:constant.gif|500px|border|frame|center|A 1:1 transformer. Here the green line isn't visible on the waveform because the voltages are identical.]]<br />
<br />
==See also==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=13395Transformers (Circuits)2015-12-05T04:25:35Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:step_up.gif|500px|A transformer that steps up voltage...fix this]]<br />
[[File:step_down.gif|500px|A transformer that steps up voltage...fix this]]<br />
[[File:constant.gif|500px|A transformer that steps up voltage...fix this]]<br />
<br />
== See also ==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=File:Step_up.gif&diff=13388File:Step up.gif2015-12-05T04:23:11Z<p>Nteissler: </p>
<hr />
<div></div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=File:Step_down.gif&diff=13386File:Step down.gif2015-12-05T04:22:47Z<p>Nteissler: </p>
<hr />
<div></div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=File:Constant.gif&diff=13383File:Constant.gif2015-12-05T04:22:08Z<p>Nteissler: </p>
<hr />
<div></div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11142Transformers (Circuits)2015-12-04T01:39:25Z<p>Nteissler: /* Circuits */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuit Diagrams==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11140Transformers (Circuits)2015-12-04T01:36:24Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Simple Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11138Transformers (Circuits)2015-12-04T01:35:42Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]<br />
<br />
[[Category: Circuits]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11135Transformers (Circuits)2015-12-04T01:34:07Z<p>Nteissler: /* See also */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
#[[Faraday's Law]] This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
#[[Inductance]] A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
#[[Gauss's Flux Theorem]] Changing the flux of a magnetic field around a coil will induce voltage.<br />
#[[Transformers from a physics standpoint]] Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]<br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11133Transformers (Circuits)2015-12-04T01:33:01Z<p>Nteissler: /* References */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[[Faraday's Law]]<br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[[Inductance]]<br />
<br />
A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
<br />
[[Gauss's Flux Theorem]]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]<br />
<br />
[http://icircuitapp.com iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11131Transformers (Circuits)2015-12-04T01:31:55Z<p>Nteissler: /* See also */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[[Faraday's Law]]<br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[[Inductance]]<br />
<br />
A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
<br />
[[Gauss's Flux Theorem]]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]<br />
<br />
iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)<br />
<br />
[http://icircuitapp.com]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11129Transformers (Circuits)2015-12-04T01:30:48Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 917-921). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]<br />
<br />
iCircuit - Electronic Circuit Simulator and Designer (available for Windows, Mac, and iOS)<br />
<br />
[http://icircuitapp.com]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11127Transformers (Circuits)2015-12-04T01:28:51Z<p>Nteissler: /* See also */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
A more in depth look at Inductance, a direct consequence of Faraday's Law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
Detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11126Transformers (Circuits)2015-12-04T01:27:37Z<p>Nteissler: /* Circuits */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
Include here: a gif of 1 to 1 transformer, step up, step down and converting AC back to DC.<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
A little more detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11122Transformers (Circuits)2015-12-04T01:26:06Z<p>Nteissler: /* See also */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
[[Transformers from a physics standpoint]]<br />
<br />
A little more detail on the material properties and physics of transformers, outside the scope of circuits.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11121Transformers (Circuits)2015-12-04T01:25:10Z<p>Nteissler: /* Voltage Ratio */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved; the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11119Transformers (Circuits)2015-12-04T01:24:45Z<p>Nteissler: /* Voltage Ratio */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which cancels and leaves <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved, so the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11117Transformers (Circuits)2015-12-04T01:24:03Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which leaves us with <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved, so the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11116Transformers (Circuits)2015-12-04T01:23:39Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which leaves us with <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
This transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved, so the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11113Transformers (Circuits)2015-12-04T01:22:46Z<p>Nteissler: /* How They Work */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> turns around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> turns around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which leaves us with <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math>.<br />
<br />
<br />
So this transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved, so the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil.<br />
<br />
The transformer described above is called a "step-up" transformer because it "ups" the voltage. There are also "step-down" transformers which reduce the voltage and have fewer turns on the secondary coil than primary coil.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11105Transformers (Circuits)2015-12-04T01:19:20Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> coils around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> coils around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>. We have <math>N_2</math> secondary coils, so the emf is <math>N_2 AdB/dt</math>. If we expand out our <math>dB/dt</math> term, we can get the emf across the second coil in a formula similar to the emf across the primary coil: <math>emf_{sec} = N_2A(\mu_0N_1/d)dI/dt</math>.<br />
<br />
===Voltage Ratio===<br />
We now can see that the ratio of the secondary to primary emf is <math>emf_{pri}/emf_{sec}</math>. This yields:<br />
<br />
<math>\frac {N_2A(\mu_0N_1/d)dI/dt}{A(\mu_0 N_1^2 /d)dI/dt}</math> which leaves us with <math>\frac {N_2}{N_1}</math> or in this case <math>\frac{200}{100}</math. So this transformer would create a emf 2 times the emf in the primary coil. Because we can't create energy from nothing, power (<math>I\Delta V</math>) must be conserved, so the double voltage in the secondary coil is accompanied by a current of half the strength of the primary coil. <br />
<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11073Transformers (Circuits)2015-12-04T00:58:38Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of self-induced emf: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
*Expanding this, we get the self-induced emf in a solenoid is: <math>\textstyle emf= \frac{\mu_0 N^2}{d}\pi R^2 \frac{d I}{d t}</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> coils around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> coils around this solenoid to form the secondary coil. If an ''alternating current'' is run through the primary coil, we get a non-zero <math>\textstyle\frac{d I}{d t}</math>We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
As stated [[#Mathematical Formulae|above]], the induced emf in the primary coil is <math>L\left|\frac{d I}{d t} \right \vert</math>. Expanding this and substituting <math>A=\pi R^2</math> for the area, we get a potential difference across the primary coil of <math>\textstyle A(\mu_0 N_1^2 /d)dI/dt</math>.<br />
<br />
===Secondary Coil===<br />
A current is induced in the secondary coil by the changing magnetic field produced by the primary coil. The magnetic field is <math>\textstyle B = \mu_0 N_1 I/d</math> and it is changing across area <math>A</math> (which is only the area of the inner coil, not the outer secondary coil. So the emf in one turn of the secondary coil is <math>A dB/dt</math>.<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11061Transformers (Circuits)2015-12-04T00:37:28Z<p>Nteissler: /* How They Work */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of an emf induced by a non-Coloumb electric field: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> coils around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> coils around this solenoid to form the secondary coil. We can now calculate the potential difference across each coil.<br />
<br />
===Primary Coil===<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=11060Transformers (Circuits)2015-12-04T00:36:11Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of an emf induced by a non-Coloumb electric field: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
==How They Work==<br />
Conversion from high to low, or low to high voltage can be accomplished using the principles discussed above. Consider a solenoid with <math>N_1=100</math> coils around a hollow cylinder of length <math>d=.3 m</math>. Now wrap <math>N_2 = 200</math> coils around this solenoid to form the secondary coil. <br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=8179Main Page2015-12-02T18:56:27Z<p>Nteissler: fixed formatting of the resources section</p>
<hr />
<div>__NOTOC__<br />
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br />
<br />
Looking to make a contribution?<br />
#Pick a specific topic from intro physics<br />
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.<br />
#Copy and paste the default [[Template]] into your new page and start editing.<br />
<br />
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Categories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Interactions===<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
**[[Ball and Spring Model of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
*[[Newton's Second Law of Motion]]<br />
*[[Newton's Third Law of Motion]]<br />
*[[Gravitational Force]]<br />
*[[Electric Force]]<br />
*[[Conservation of Charge]]<br />
*[[Terminal Speed]]<br />
*[[Simple Harmonic Motion]]<br />
*[[Speed and Velocity]]<br />
*[[Electric Polarization]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
*[[2-Dimensional Motion]]<br />
*[[Center of Mass]]<br />
*[[Reaction Time]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Theory===<br />
<div class="mw-collapsible-content"><br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[Big Bang Theory]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
*[[Atomic Theory]]<br />
*[[Wave-Particle Duality]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Notable Scientists===<br />
<div class="mw-collapsible-content"><br />
*[[Christian Doppler]]<br />
*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Joseph Henry]]<br />
*[[Michael Faraday]]<br />
*[[J.J. Thomson]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
*[[Oliver Heaviside]]<br />
*[[Rosalind Franklin]]<br />
*[[Erwin Schrödinger]]<br />
*[[Enrico Fermi]]<br />
*[[Robert J. Van de Graaff]]<br />
*[[Charles de Coulomb]]<br />
*[[Hans Christian Ørsted]]<br />
*[[Philo Farnsworth]]<br />
*[[Niels Bohr]]<br />
*[[Georg Ohm]]<br />
*[[Galileo Galilei]]<br />
*[[Gustav Kirchhoff]]<br />
*[[Max Planck]]<br />
*[[Heinrich Hertz]]<br />
*[[Edwin Hall]]<br />
*[[James Watt]]<br />
*[[Count Alessandro Volta]]<br />
*[[Josiah Willard Gibbs]]<br />
*[[Richard Phillips Feynman]]<br />
*[[Sir David Brewster]]<br />
*[[Daniel Bernoulli]]<br />
*[[William Thomson]]<br />
*[[Leonhard Euler]]<br />
*[[Robert Fox Bacher]]<br />
*[[Stephen Hawking]]<br />
*[[Amedeo Avogadro]]<br />
*[[Wilhelm Conrad Roentgen]]<br />
*[[Pierre Laplace]]<br />
*[[Thomas Edison]]<br />
*[[Hendrik Lorentz]]<br />
*[[Jean-Baptiste Biot]]<br />
*[[Lise Meitner]]<br />
*[[Lisa Randall]]<br />
*[[Felix Savart]]<br />
*[[Heinrich Lenz]]<br />
*[[Max Born]]<br />
*[[Archimedes]]<br />
*[[Jean Baptiste Biot]]<br />
*[[Carl Sagan]]<br />
*[[Eugene Wigner]]<br />
*[[Marie Curie]]<br />
*[[Pierre Curie]]<br />
*[[Werner Heisenberg]]<br />
*[[Johannes Diderik van der Waals]]<br />
*[[Louis de Broglie]]<br />
*[[Aristotle]]<br />
*[[Émilie du Châtelet]]<br />
*[[Blaise Pascal]]<br />
*[[Benjamin Franklin]]<br />
*[[James Chadwick]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Properties of Matter===<br />
<div class="mw-collapsible-content"><br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Density]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
*[[Heat Capacity]]<br />
*[[Specific Heat]]<br />
*[[Wavelength]]<br />
*[[Conductivity]]<br />
*[[Malleability]]<br />
*[[Weight]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Higgs Boson]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Contact Interactions===<br />
<div class="mw-collapsible-content"><br />
* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Compression or Normal Force]]<br />
* [[Length and Stiffness of an Interatomic Bond]]<br />
* [[Speed of Sound in a Solid]]<br />
* [[Iterative Prediction of Spring-Mass System]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[Vectors]]<br />
* [[Kinematics]]<br />
* [[Conservation of Momentum]]<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Impulse Momentum]]<br />
* [[Curving Motion]]<br />
* [[Multi-particle Analysis of Momentum]]<br />
* [[Iterative Prediction]]<br />
* [[Newton's Laws and Linear Momentum]]<br />
* [[Net Force]]<br />
* [[Center of Mass]]<br />
* [[Momentum at High Speeds]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Angular Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[The Moments of Inertia]]<br />
* [[Moment of Inertia for a ring]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
* [[Systems with Zero Torque]]<br />
* [[Systems with Nonzero Torque]]<br />
* [[Right Hand Rule]]<br />
* [[Angular Velocity]]<br />
* [[Predicting the Position of a Rotating System]]<br />
* [[Translational Angular Momentum]]<br />
* [[The Angular Momentum Principle]]<br />
* [[Rotational Angular Momentum]]<br />
* [[Total Angular Momentum]]<br />
* [[Gyroscopes]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Energy===<br />
<div class="mw-collapsible-content"><br />
*[[The Photoelectric Effect]]<br />
*[[Photons]]<br />
*[[The Energy Principle]]<br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
*[[Spring Potential Energy]]<br />
**[[Ball and Spring Model]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Franck-Hertz Experiment]]<br />
*[[Power (Mechanical)]]<br />
*[[Energy Graphs]]<br />
*[[Air Resistance]]<br />
*[[Electronic Energy Levels]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Specific Heat Capacity]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Energy Density]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Path Independence of Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Collisions===<br />
<div class="mw-collapsible-content"><br />
*[[Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Frame of Reference]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Fields===<br />
<div class="mw-collapsible-content"><br />
* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
** [[Charged Cylinder]]<br />
** [[Charged Hollow Cylinder]]<br />
**[[A Solid Sphere Charged Throughout Its Volume]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference Path Independence]]<br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Potential Difference of point charge in a non-Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
**[[Potential Difference in an Insulator]]<br />
**[[Energy Density and Electric Field]]<br />
** [[Systems of Charged Objects]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
**[[Polarization of an Atom]]<br />
*[[Charge Motion in Metals]]<br />
*[[Charge Transfer]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Magnetic Field of a Long Straight Wire]]<br />
**[[Magnetic Field of a Loop]]<br />
**[[Magnetic Field of a Solenoid]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Dipole Moment]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Biot-Savart Law for Currents]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
**[[Moving Point Charge]]<br />
**[[Non-Coulomb Electric Field]]<br />
**[[Motors and Generators]]<br />
**[[Solenoid Applications]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Simple Circuits===<br />
<div class="mw-collapsible-content"><br />
*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Charging and Discharging a Capacitor]]<br />
*[[Thin and Thick Wires]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Resistivity]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
**[[AC]]<br />
*[[Ohm's Law]]<br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[RC]]<br />
*[[Charge in a RC Circuit]]<br />
*[[Current in a RC circuit]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
*[[Surface Charge Distributions]]<br />
*[[Feedback]]<br />
*[[Transformers (Circuits)]]<br />
*[[Resistors and Conductivity]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Maxwell's Equations===<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Ampere's Law]]<br />
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
**[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Faraday's Law]]<br />
**[[Curly Electric Fields]]<br />
**[[Inductance]]<br />
***[[Transformers from a physics standpoint]]<br />
***[[Energy Density]]<br />
**[[Lenz's Law]]<br />
***[[Lenz Effect and the Jumping Ring]]<br />
**[[Motional Emf using Faraday's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Superconductors]]<br />
**[[Meissner effect]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Radiation===<br />
<div class="mw-collapsible-content"><br />
*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
*[[Lenses]]<br />
*[[Energy and Momentum Analysis in Radiation]]<br />
*[[Electromagnetic Propagation]]<br />
**[[Wavelength and Frequency]]<br />
*[[Snell's Law]]<br />
*[[Effects of Radiation on Matter]]<br />
*[[Light Propagation Through a Medium]]<br />
*[[Light Scaterring: Why is the Sky Blue]]<br />
*[[Light Refraction: Bending of light]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Sound===<br />
<div class="mw-collapsible-content"><br />
*[[Doppler Effect]]<br />
*[[Nature, Behavior, and Properties of Sound]]<br />
*[[Resonance]]<br />
*[[Sound Barrier]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Waves===<br />
<div class="mw-collapsible-content"><br />
*[[Multisource Interference: Diffraction]]<br />
*[[Standing waves]]<br />
*[[Gravitational waves]]<br />
*[[Wave-Particle Duality]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Real Life Applications of Electromagnetic Principles===<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Junkyard Cranes]]<br />
*[[Maglev Trains]]<br />
</div><br />
</div><br />
<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=8156Main Page2015-12-02T18:48:20Z<p>Nteissler: /* Maxwell's Equations */</p>
<hr />
<div>__NOTOC__<br />
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br />
<br />
Looking to make a contribution?<br />
#Pick a specific topic from intro physics<br />
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.<br />
#Copy and paste the default [[Template]] into your new page and start editing.<br />
<br />
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Categories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Interactions===<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
**[[Ball and Spring Model of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
*[[Newton's Second Law of Motion]]<br />
*[[Newton's Third Law of Motion]]<br />
*[[Gravitational Force]]<br />
*[[Electric Force]]<br />
*[[Conservation of Charge]]<br />
*[[Terminal Speed]]<br />
*[[Simple Harmonic Motion]]<br />
*[[Speed and Velocity]]<br />
*[[Electric Polarization]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
*[[2-Dimensional Motion]]<br />
*[[Center of Mass]]<br />
*[[Reaction Time]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Theory===<br />
<div class="mw-collapsible-content"><br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[Big Bang Theory]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
*[[Atomic Theory]]<br />
*[[Wave-Particle Duality]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Notable Scientists===<br />
<div class="mw-collapsible-content"><br />
*[[Christian Doppler]]<br />
*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Joseph Henry]]<br />
*[[Michael Faraday]]<br />
*[[J.J. Thomson]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
*[[Oliver Heaviside]]<br />
*[[Rosalind Franklin]]<br />
*[[Erwin Schrödinger]]<br />
*[[Enrico Fermi]]<br />
*[[Robert J. Van de Graaff]]<br />
*[[Charles de Coulomb]]<br />
*[[Hans Christian Ørsted]]<br />
*[[Philo Farnsworth]]<br />
*[[Niels Bohr]]<br />
*[[Georg Ohm]]<br />
*[[Galileo Galilei]]<br />
*[[Gustav Kirchhoff]]<br />
*[[Max Planck]]<br />
*[[Heinrich Hertz]]<br />
*[[Edwin Hall]]<br />
*[[James Watt]]<br />
*[[Count Alessandro Volta]]<br />
*[[Josiah Willard Gibbs]]<br />
*[[Richard Phillips Feynman]]<br />
*[[Sir David Brewster]]<br />
*[[Daniel Bernoulli]]<br />
*[[William Thomson]]<br />
*[[Leonhard Euler]]<br />
*[[Robert Fox Bacher]]<br />
*[[Stephen Hawking]]<br />
*[[Amedeo Avogadro]]<br />
*[[Wilhelm Conrad Roentgen]]<br />
*[[Pierre Laplace]]<br />
*[[Thomas Edison]]<br />
*[[Hendrik Lorentz]]<br />
*[[Jean-Baptiste Biot]]<br />
*[[Lise Meitner]]<br />
*[[Lisa Randall]]<br />
*[[Felix Savart]]<br />
*[[Heinrich Lenz]]<br />
*[[Max Born]]<br />
*[[Archimedes]]<br />
*[[Jean Baptiste Biot]]<br />
*[[Carl Sagan]]<br />
*[[Eugene Wigner]]<br />
*[[Marie Curie]]<br />
*[[Pierre Curie]]<br />
*[[Werner Heisenberg]]<br />
*[[Johannes Diderik van der Waals]]<br />
*[[Louis de Broglie]]<br />
*[[Aristotle]]<br />
*[[Émilie du Châtelet]]<br />
*[[Blaise Pascal]]<br />
*[[Benjamin Franklin]]<br />
*[[James Chadwick]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Properties of Matter===<br />
<div class="mw-collapsible-content"><br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Density]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
*[[Heat Capacity]]<br />
*[[Specific Heat]]<br />
*[[Wavelength]]<br />
*[[Conductivity]]<br />
*[[Malleability]]<br />
*[[Weight]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Higgs Boson]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Contact Interactions===<br />
<div class="mw-collapsible-content"><br />
* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Compression or Normal Force]]<br />
* [[Length and Stiffness of an Interatomic Bond]]<br />
* [[Speed of Sound in a Solid]]<br />
* [[Iterative Prediction of Spring-Mass System]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[Vectors]]<br />
* [[Kinematics]]<br />
* [[Conservation of Momentum]]<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Impulse Momentum]]<br />
* [[Curving Motion]]<br />
* [[Multi-particle Analysis of Momentum]]<br />
* [[Iterative Prediction]]<br />
* [[Newton's Laws and Linear Momentum]]<br />
* [[Net Force]]<br />
* [[Center of Mass]]<br />
* [[Momentum at High Speeds]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Angular Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[The Moments of Inertia]]<br />
* [[Moment of Inertia for a ring]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
* [[Systems with Zero Torque]]<br />
* [[Systems with Nonzero Torque]]<br />
* [[Right Hand Rule]]<br />
* [[Angular Velocity]]<br />
* [[Predicting the Position of a Rotating System]]<br />
* [[Translational Angular Momentum]]<br />
* [[The Angular Momentum Principle]]<br />
* [[Rotational Angular Momentum]]<br />
* [[Total Angular Momentum]]<br />
* [[Gyroscopes]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Energy===<br />
<div class="mw-collapsible-content"><br />
*[[The Photoelectric Effect]]<br />
*[[Photons]]<br />
*[[The Energy Principle]]<br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
*[[Spring Potential Energy]]<br />
**[[Ball and Spring Model]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Franck-Hertz Experiment]]<br />
*[[Power (Mechanical)]]<br />
*[[Energy Graphs]]<br />
*[[Air Resistance]]<br />
*[[Electronic Energy Levels]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Specific Heat Capacity]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Energy Density]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Path Independence of Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Collisions===<br />
<div class="mw-collapsible-content"><br />
*[[Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Frame of Reference]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Fields===<br />
<div class="mw-collapsible-content"><br />
* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
** [[Charged Cylinder]]<br />
** [[Charged Hollow Cylinder]]<br />
**[[A Solid Sphere Charged Throughout Its Volume]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference Path Independence]]<br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Potential Difference of point charge in a non-Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
**[[Potential Difference in an Insulator]]<br />
**[[Energy Density and Electric Field]]<br />
** [[Systems of Charged Objects]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
**[[Polarization of an Atom]]<br />
*[[Charge Motion in Metals]]<br />
*[[Charge Transfer]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Magnetic Field of a Long Straight Wire]]<br />
**[[Magnetic Field of a Loop]]<br />
**[[Magnetic Field of a Solenoid]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Dipole Moment]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Biot-Savart Law for Currents]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
**[[Moving Point Charge]]<br />
**[[Non-Coulomb Electric Field]]<br />
**[[Motors and Generators]]<br />
**[[Solenoid Applications]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Simple Circuits===<br />
<div class="mw-collapsible-content"><br />
*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Charging and Discharging a Capacitor]]<br />
*[[Thin and Thick Wires]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Resistivity]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
**[[AC]]<br />
*[[Ohm's Law]]<br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[RC]]<br />
*[[Charge in a RC Circuit]]<br />
*[[Current in a RC circuit]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
*[[Surface Charge Distributions]]<br />
*[[Feedback]]<br />
*[[Transformers (Circuits)]]<br />
*[[Resistors and Conductivity]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Maxwell's Equations===<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Ampere's Law]]<br />
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
**[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Faraday's Law]]<br />
**[[Curly Electric Fields]]<br />
**[[Inductance]]<br />
***[[Transformers from a physics standpoint]]<br />
***[[Energy Density]]<br />
**[[Lenz's Law]]<br />
***[[Lenz Effect and the Jumping Ring]]<br />
**[[Motional Emf using Faraday's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Superconductors]]<br />
**[[Meissner effect]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Radiation===<br />
<div class="mw-collapsible-content"><br />
*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
*[[Lenses]]<br />
*[[Energy and Momentum Analysis in Radiation]]<br />
*[[Electromagnetic Propagation]]<br />
**[[Wavelength and Frequency]]<br />
*[[Snell's Law]]<br />
*[[Effects of Radiation on Matter]]<br />
*[[Light Propagation Through a Medium]]<br />
*[[Light Scaterring: Why is the Sky Blue]]<br />
*[[Light Refraction: Bending of light]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Sound===<br />
<div class="mw-collapsible-content"><br />
*[[Doppler Effect]]<br />
*[[Nature, Behavior, and Properties of Sound]]<br />
*[[Resonance]]<br />
*[[Sound Barrier]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Waves===<br />
<div class="mw-collapsible-content"><br />
*[[Multisource Interference: Diffraction]]<br />
*[[Standing waves]]<br />
*[[Gravitational waves]]<br />
*[[Wave-Particle Duality]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Real Life Applications of Electromagnetic Principles===<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Junkyard Cranes]]<br />
*[[Maglev Trains]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=8152Main Page2015-12-02T18:46:58Z<p>Nteissler: /* Simple Circuits */</p>
<hr />
<div>__NOTOC__<br />
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br />
<br />
Looking to make a contribution?<br />
#Pick a specific topic from intro physics<br />
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.<br />
#Copy and paste the default [[Template]] into your new page and start editing.<br />
<br />
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Categories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Interactions===<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
**[[Ball and Spring Model of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
*[[Newton's Second Law of Motion]]<br />
*[[Newton's Third Law of Motion]]<br />
*[[Gravitational Force]]<br />
*[[Electric Force]]<br />
*[[Conservation of Charge]]<br />
*[[Terminal Speed]]<br />
*[[Simple Harmonic Motion]]<br />
*[[Speed and Velocity]]<br />
*[[Electric Polarization]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
*[[2-Dimensional Motion]]<br />
*[[Center of Mass]]<br />
*[[Reaction Time]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Theory===<br />
<div class="mw-collapsible-content"><br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[Big Bang Theory]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
*[[Atomic Theory]]<br />
*[[Wave-Particle Duality]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Notable Scientists===<br />
<div class="mw-collapsible-content"><br />
*[[Christian Doppler]]<br />
*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Joseph Henry]]<br />
*[[Michael Faraday]]<br />
*[[J.J. Thomson]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
*[[Oliver Heaviside]]<br />
*[[Rosalind Franklin]]<br />
*[[Erwin Schrödinger]]<br />
*[[Enrico Fermi]]<br />
*[[Robert J. Van de Graaff]]<br />
*[[Charles de Coulomb]]<br />
*[[Hans Christian Ørsted]]<br />
*[[Philo Farnsworth]]<br />
*[[Niels Bohr]]<br />
*[[Georg Ohm]]<br />
*[[Galileo Galilei]]<br />
*[[Gustav Kirchhoff]]<br />
*[[Max Planck]]<br />
*[[Heinrich Hertz]]<br />
*[[Edwin Hall]]<br />
*[[James Watt]]<br />
*[[Count Alessandro Volta]]<br />
*[[Josiah Willard Gibbs]]<br />
*[[Richard Phillips Feynman]]<br />
*[[Sir David Brewster]]<br />
*[[Daniel Bernoulli]]<br />
*[[William Thomson]]<br />
*[[Leonhard Euler]]<br />
*[[Robert Fox Bacher]]<br />
*[[Stephen Hawking]]<br />
*[[Amedeo Avogadro]]<br />
*[[Wilhelm Conrad Roentgen]]<br />
*[[Pierre Laplace]]<br />
*[[Thomas Edison]]<br />
*[[Hendrik Lorentz]]<br />
*[[Jean-Baptiste Biot]]<br />
*[[Lise Meitner]]<br />
*[[Lisa Randall]]<br />
*[[Felix Savart]]<br />
*[[Heinrich Lenz]]<br />
*[[Max Born]]<br />
*[[Archimedes]]<br />
*[[Jean Baptiste Biot]]<br />
*[[Carl Sagan]]<br />
*[[Eugene Wigner]]<br />
*[[Marie Curie]]<br />
*[[Pierre Curie]]<br />
*[[Werner Heisenberg]]<br />
*[[Johannes Diderik van der Waals]]<br />
*[[Louis de Broglie]]<br />
*[[Aristotle]]<br />
*[[Émilie du Châtelet]]<br />
*[[Blaise Pascal]]<br />
*[[Benjamin Franklin]]<br />
*[[James Chadwick]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Properties of Matter===<br />
<div class="mw-collapsible-content"><br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Density]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
*[[Heat Capacity]]<br />
*[[Specific Heat]]<br />
*[[Wavelength]]<br />
*[[Conductivity]]<br />
*[[Malleability]]<br />
*[[Weight]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Higgs Boson]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Contact Interactions===<br />
<div class="mw-collapsible-content"><br />
* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Compression or Normal Force]]<br />
* [[Length and Stiffness of an Interatomic Bond]]<br />
* [[Speed of Sound in a Solid]]<br />
* [[Iterative Prediction of Spring-Mass System]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[Vectors]]<br />
* [[Kinematics]]<br />
* [[Conservation of Momentum]]<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Impulse Momentum]]<br />
* [[Curving Motion]]<br />
* [[Multi-particle Analysis of Momentum]]<br />
* [[Iterative Prediction]]<br />
* [[Newton's Laws and Linear Momentum]]<br />
* [[Net Force]]<br />
* [[Center of Mass]]<br />
* [[Momentum at High Speeds]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Angular Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[The Moments of Inertia]]<br />
* [[Moment of Inertia for a ring]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
* [[Systems with Zero Torque]]<br />
* [[Systems with Nonzero Torque]]<br />
* [[Right Hand Rule]]<br />
* [[Angular Velocity]]<br />
* [[Predicting the Position of a Rotating System]]<br />
* [[Translational Angular Momentum]]<br />
* [[The Angular Momentum Principle]]<br />
* [[Rotational Angular Momentum]]<br />
* [[Total Angular Momentum]]<br />
* [[Gyroscopes]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Energy===<br />
<div class="mw-collapsible-content"><br />
*[[The Photoelectric Effect]]<br />
*[[Photons]]<br />
*[[The Energy Principle]]<br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
*[[Spring Potential Energy]]<br />
**[[Ball and Spring Model]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Franck-Hertz Experiment]]<br />
*[[Power (Mechanical)]]<br />
*[[Energy Graphs]]<br />
*[[Air Resistance]]<br />
*[[Electronic Energy Levels]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Specific Heat Capacity]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Energy Density]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Path Independence of Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Collisions===<br />
<div class="mw-collapsible-content"><br />
*[[Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Frame of Reference]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Fields===<br />
<div class="mw-collapsible-content"><br />
* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
** [[Charged Cylinder]]<br />
** [[Charged Hollow Cylinder]]<br />
**[[A Solid Sphere Charged Throughout Its Volume]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference Path Independence]]<br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Potential Difference of point charge in a non-Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
**[[Potential Difference in an Insulator]]<br />
**[[Energy Density and Electric Field]]<br />
** [[Systems of Charged Objects]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
**[[Polarization of an Atom]]<br />
*[[Charge Motion in Metals]]<br />
*[[Charge Transfer]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Magnetic Field of a Long Straight Wire]]<br />
**[[Magnetic Field of a Loop]]<br />
**[[Magnetic Field of a Solenoid]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Dipole Moment]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Biot-Savart Law for Currents]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
**[[Moving Point Charge]]<br />
**[[Non-Coulomb Electric Field]]<br />
**[[Motors and Generators]]<br />
**[[Solenoid Applications]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Simple Circuits===<br />
<div class="mw-collapsible-content"><br />
*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Charging and Discharging a Capacitor]]<br />
*[[Thin and Thick Wires]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Resistivity]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
**[[AC]]<br />
*[[Ohm's Law]]<br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[RC]]<br />
*[[Charge in a RC Circuit]]<br />
*[[Current in a RC circuit]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
*[[Surface Charge Distributions]]<br />
*[[Feedback]]<br />
*[[Transformers (Circuits)]]<br />
*[[Resistors and Conductivity]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Maxwell's Equations===<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Ampere's Law]]<br />
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
**[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Faraday's Law]]<br />
**[[Curly Electric Fields]]<br />
**[[Inductance]]<br />
***[[Transformers]]<br />
***[[Transformers from a physics standpoint]]<br />
***[[Energy Density]]<br />
**[[Lenz's Law]]<br />
***[[Lenz Effect and the Jumping Ring]]<br />
**[[Motional Emf using Faraday's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Superconductors]]<br />
**[[Meissner effect]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Radiation===<br />
<div class="mw-collapsible-content"><br />
*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
*[[Lenses]]<br />
*[[Energy and Momentum Analysis in Radiation]]<br />
*[[Electromagnetic Propagation]]<br />
**[[Wavelength and Frequency]]<br />
*[[Snell's Law]]<br />
*[[Effects of Radiation on Matter]]<br />
*[[Light Propagation Through a Medium]]<br />
*[[Light Scaterring: Why is the Sky Blue]]<br />
*[[Light Refraction: Bending of light]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Sound===<br />
<div class="mw-collapsible-content"><br />
*[[Doppler Effect]]<br />
*[[Nature, Behavior, and Properties of Sound]]<br />
*[[Resonance]]<br />
*[[Sound Barrier]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Waves===<br />
<div class="mw-collapsible-content"><br />
*[[Multisource Interference: Diffraction]]<br />
*[[Standing waves]]<br />
*[[Gravitational waves]]<br />
*[[Wave-Particle Duality]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Real Life Applications of Electromagnetic Principles===<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Junkyard Cranes]]<br />
*[[Maglev Trains]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=8147Transformers (Circuits)2015-12-02T18:46:12Z<p>Nteissler: Nteissler moved page Transformers to Transformers (Circuits): there will exist two transformers page, one focusing on circuit and one focusing on the physics of inductance/history of transformers</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of an emf induced by a non-Coloumb electric field: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=8143Transformers (Circuits)2015-12-02T18:44:41Z<p>Nteissler: /* Mathematical Formulae */</p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
* Magnetic Field Inside a Solenoid: <math>B=\frac{\mu_0 N I}{d}</math><br />
::Where <math>\textstyle N</math> is the number of coils and <math>\textstyle d</math> is the length of the solenoid.<br />
<br />
* Magnitude of an emf induced by a non-Coloumb electric field: <math>\textstyle \left|emf_{ind}\right \vert=L\left|\frac{d I}{d t} \right \vert</math><br />
:: Where <math>L</math> is the proportionality constant called the "inductance" or "self-inductance" which equals <math>\textstyle \frac{\mu_0 N^2}{d}\pi R^2</math><br />
<br />
* Finally, remember your units. <math>emf</math> is measured in volts, self-inductance is <math>\textstyle(V•s/A)</math> or the "henry" (H), and <math>B</math> is measured in Tesla (T) or <math>\textstyle(\frac{kg}{s^2 A})</math><br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=8063Transformers (Circuits)2015-12-02T16:35:56Z<p>Nteissler: </p>
<hr />
<div>Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7644Transformers (Circuits)2015-12-02T04:01:05Z<p>Nteissler: /* Circuits */</p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png|300px]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7642Transformers (Circuits)2015-12-02T04:00:42Z<p>Nteissler: /* Circuits */</p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png]]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7640Transformers (Circuits)2015-12-02T04:00:32Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
<br />
==Circuits==<br />
[[File:tform_circuit_1.png\]]<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=File:Tform_circuit_1.png&diff=7637File:Tform circuit 1.png2015-12-02T03:59:36Z<p>Nteissler: </p>
<hr />
<div></div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7632Transformers (Circuits)2015-12-02T03:58:06Z<p>Nteissler: /* Mathematical Formulae */</p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7627Transformers (Circuits)2015-12-02T03:55:38Z<p>Nteissler: /* Inductance */</p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle (dB/dt)</math> produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:<br />
<br />
<math align="center">|emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert </math><br />
<br />
Or that a changing magnetic field through an area produces a non-Coloumb electric field.<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7594Transformers (Circuits)2015-12-02T03:32:47Z<p>Nteissler: /* Inductance */</p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field <math>\textstyle dB/dt</math> produced by varying the current through the coil.<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7591Transformers (Circuits)2015-12-02T03:28:44Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Inductance===<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7589Transformers (Circuits)2015-12-02T03:26:18Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Induction===<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gauss's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html] <br />
<br />
[https://en.wikipedia.org/wiki/Transformer https://en.wikipedia.org/wiki/Transformer]<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7587Transformers (Circuits)2015-12-02T03:25:39Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Induction===<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gaus's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html] <br />
<br />
[https://en.wikipedia.org/wiki/Transformer https://en.wikipedia.org/wiki/Transformer]<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7586Transformers (Circuits)2015-12-02T03:25:28Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
[[File:Transcon.gif|2000px|thumb|right|Transformer Concept Map]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Induction===<br />
<br />
===Mathematical Formulae===<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
<br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gaus's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html] <br />
<br />
[https://en.wikipedia.org/wiki/Transformer https://en.wikipedia.org/wiki/Transformer]<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7583Transformers (Circuits)2015-12-02T03:24:16Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
[[File:Transcon.gif|2000px|thumb|right|Transformer Concept Map]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==Background==<br />
<br />
===Induction===<br />
<br />
===Mathematical Formulae===<br />
<br />
===A Mathematical Model===<br />
<br />
For a "step-down" transformer (one that converts from high to low voltage and increases current):<br />
<br />
If a solenoid is built wrapping <math>{N}_{1}</math> turns around a hollow cylinder for the primary coil, and wrapping <math>{N}_{2}</math> turns around the outside of the secondary coil, and then connecting the primary coil to a an AC power supply, the emf that will develop in the secondary coil will be as follows:<br />
<br />
The magnetic field made by the primary coil: <math>B = \frac{\mu_0IN_1}{d}</math><br />
The cross-sectional area of the solenoid is A, so the emf in one turn of the secondary coil is: <math>\frac{AdB}{dt}</math><br />
The total emf in the secondary coil is <math>{N}_{2}</math> times the emf in one turn, so the potential difference across the secondary coil is: <br />
<math>{N}_{2}A(mu_0{N}_{1}/d)dI/dt</math> .<br />
<br />
The potential difference across the primary coil is <math>\frac{LdI}{dt}</math>, where <math>L = \frac{\mu_0AIN_1^2}{d}</math>, so the potential difference across the primary coil is: <math>A({\mu_0}IN_1^2/d)dI/dt</math><br />
<br />
Comparing <math> emf_2={N}_{2}A(mu_0{N}_{1}/d)dI/dt</math> with <math> emf_1= A(mu_0{N}_{1}^2/d)dI/dt</math>, we see that <math> emf_2= ({N}_{2}/{N}_{1})emf_1</math>. The ratio of the number of turns determines the change in voltage.<br />
<br />
Faraday's law applied to a transformer can be written as: <math>\frac{V_s}{V_p}= \frac{N_s}{N_p}</math>, where the subscripts refer to primary and secondary coils. <br />
<br />
<br />
Because energy is conserved and power is <math>I \Delta {E}</math>, the smaller voltage in the secondary coil is accompanied by a larger current. This can be written as: <math>P_p= V_pI_p=V_sI_s = P_s</math>. <br />
<br />
In the case of a "step-up" transformer, the primary coil has few turn and the secondary many, therefore increasing the voltage and decreasing the current.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
A transformer has a primary coil with 102 turns and a secondary coil of 360 turns. The AC voltage across the primary coil has a maximum of 124 V and the AC current through the primary coil has a maximum of 3 A. What are the maximum values of the voltage and current for the secondary coil? <br />
<br />
<math>{V_s}=? {V_p}= 124V {N_s}= 360 {N_p}= 102</math>.<br />
<br />
<math>\frac{V_s}{V_p}= \frac{N_s}{N_p}</math>.<br />
<br />
<math>\frac{V_s}{124V}= \frac{360}{102}</math>.<br />
<br />
<math>{V_s}= 438V</math>.<br />
<br />
<br />
<math>P_p= V_pI_p=V_sI_s = P_s</math>. <br />
<br />
<math> V_p=124V I_p=3A V_s= 438V I_s = ?</math>. <br />
<br />
<math> (124V)(3A)= (438V)I_s </math>. <br />
<br />
<math>I_s = 0.85A</math>. <br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
The property of induction was discovered in the 1830's but it wasn't until 1886 that William Stanley, working for Westinghouse, built the first reliable commercial transformer. It was first designed and used in both experimental and commercial systems by Ottó Bláthy, Miksa Déri, Károly Zipernowsky of the Austro-Hungarian Empire. The first AC power system that used the modern transformer was in Great Barrington, Massachusetts in 1886. In 1891 mastermind Mikhail Dobrovsky designed and demonstrated his 3 phase transformers in the Electro-Technical Exposition at Frankfurt, Germany. <br />
<br />
DC power was mainly used in the 1880's but it was hard to transmit over distance because it requires high voltage and a thin wire or low voltage and a wide wire. High voltage on DC is very dangerous, and with low voltage the wire would be so thick that it would be impractical. With AC power, high voltage is also used to move electricity down a long wire. AC is more practical, however, because once the power reaches the destination, a transformer can be used to change the voltage down to a manageable level. <br />
== See also ==<br />
<br />
[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
<br />
This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
<br />
[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
<br />
Inductance is another property of an electrical conductor derived from Faraday's law. <br />
<br />
[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gaus's Flux Theorem]<br />
<br />
Changing the flux of a magnetic field around a coil will induce voltage.<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html] <br />
<br />
[https://en.wikipedia.org/wiki/Transformer https://en.wikipedia.org/wiki/Transformer]<br />
<br />
[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
<br />
==References==<br />
<br />
Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html<br />
<br />
http://www.edisontechcenter.org/Transformers.html<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nteisslerhttp://www.physicsbook.gatech.edu/index.php?title=Transformers_(Circuits)&diff=7575Transformers (Circuits)2015-12-02T03:22:24Z<p>Nteissler: </p>
<hr />
<div><br />
[[File:Screenshot_creation.png]]<br />
[[File:Transcon.gif|2000px|thumb|right|Transformer Concept Map]]<br />
<br />
Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer. <br />
<br />
==The Main Idea==<br />
<br />
[[File:Transf.gif|2000px|thumb|right|Transformer and Faraday's Law]]<br />
<br />
From Faraday's law as well as conservation of energy we see that an ideal transformer the voltage ratio is equal to the turns ratio, and power in equals power out. Transformers uses both of these to convert from either high to low or low to high voltages. <br />
<br />
===A Mathematical Model===<br />
<br />
For a "step-down" transformer (one that converts from high to low voltage and increases current):<br />
<br />
If a solenoid is built wrapping <math>{N}_{1}</math> turns around a hollow cylinder for the primary coil, and wrapping <math>{N}_{2}</math> turns around the outside of the secondary coil, and then connecting the primary coil to a an AC power supply, the emf that will develop in the secondary coil will be as follows:<br />
<br />
The magnetic field made by the primary coil: <math>B = \frac{\mu_0IN_1}{d}</math><br />
The cross-sectional area of the solenoid is A, so the emf in one turn of the secondary coil is: <math>\frac{AdB}{dt}</math><br />
The total emf in the secondary coil is <math>{N}_{2}</math> times the emf in one turn, so the potential difference across the secondary coil is: <br />
<math>{N}_{2}A(mu_0{N}_{1}/d)dI/dt</math> .<br />
<br />
The potential difference across the primary coil is <math>\frac{LdI}{dt}</math>, where <math>L = \frac{\mu_0AIN_1^2}{d}</math>, so the potential difference across the primary coil is: <math>A({\mu_0}IN_1^2/d)dI/dt</math><br />
<br />
Comparing <math> emf_2={N}_{2}A(mu_0{N}_{1}/d)dI/dt</math> with <math> emf_1= A(mu_0{N}_{1}^2/d)dI/dt</math>, we see that <math> emf_2= ({N}_{2}/{N}_{1})emf_1</math>. The ratio of the number of turns determines the change in voltage.<br />
<br />
Faraday's law applied to a transformer can be written as: <math>\frac{V_s}{V_p}= \frac{N_s}{N_p}</math>, where the subscripts refer to primary and secondary coils. <br />
<br />
<br />
Because energy is conserved and power is <math>I \Delta {E}</math>, the smaller voltage in the secondary coil is accompanied by a larger current. This can be written as: <math>P_p= V_pI_p=V_sI_s = P_s</math>. <br />
<br />
In the case of a "step-up" transformer, the primary coil has few turn and the secondary many, therefore increasing the voltage and decreasing the current.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
A transformer has a primary coil with 102 turns and a secondary coil of 360 turns. The AC voltage across the primary coil has a maximum of 124 V and the AC current through the primary coil has a maximum of 3 A. What are the maximum values of the voltage and current for the secondary coil? <br />
<br />
<math>{V_s}=? {V_p}= 124V {N_s}= 360 {N_p}= 102</math>.<br />
<br />
<math>\frac{V_s}{V_p}= \frac{N_s}{N_p}</math>.<br />
<br />
<math>\frac{V_s}{124V}= \frac{360}{102}</math>.<br />
<br />
<math>{V_s}= 438V</math>.<br />
<br />
<br />
<math>P_p= V_pI_p=V_sI_s = P_s</math>. <br />
<br />
<math> V_p=124V I_p=3A V_s= 438V I_s = ?</math>. <br />
<br />
<math> (124V)(3A)= (438V)I_s </math>. <br />
<br />
<math>I_s = 0.85A</math>. <br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
The property of induction was discovered in the 1830's but it wasn't until 1886 that William Stanley, working for Westinghouse, built the first reliable commercial transformer. It was first designed and used in both experimental and commercial systems by Ottó Bláthy, Miksa Déri, Károly Zipernowsky of the Austro-Hungarian Empire. The first AC power system that used the modern transformer was in Great Barrington, Massachusetts in 1886. In 1891 mastermind Mikhail Dobrovsky designed and demonstrated his 3 phase transformers in the Electro-Technical Exposition at Frankfurt, Germany. <br />
<br />
DC power was mainly used in the 1880's but it was hard to transmit over distance because it requires high voltage and a thin wire or low voltage and a wide wire. High voltage on DC is very dangerous, and with low voltage the wire would be so thick that it would be impractical. With AC power, high voltage is also used to move electricity down a long wire. AC is more practical, however, because once the power reaches the destination, a transformer can be used to change the voltage down to a manageable level. <br />
== See also ==<br />
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[http://www.physicsbook.gatech.edu/Faraday's_Law Faraday's Law] <br />
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This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology. <br />
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[http://www.physicsbook.gatech.edu/Inductance Inductance]<br />
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Inductance is another property of an electrical conductor derived from Faraday's law. <br />
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[http://www.physicsbook.gatech.edu/Gauss's_Flux_Theorem Gaus's Flux Theorem]<br />
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Changing the flux of a magnetic field around a coil will induce voltage.<br />
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===Further reading===<br />
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Books, Articles or other print media on this topic<br />
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===External links===<br />
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[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html] <br />
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[https://en.wikipedia.org/wiki/Transformer https://en.wikipedia.org/wiki/Transformer]<br />
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[http://www.edisontechcenter.org/Transformers.html http://www.edisontechcenter.org/Transformers.html]<br />
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==References==<br />
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Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons. <br />
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http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html<br />
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http://www.edisontechcenter.org/Transformers.html<br />
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