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[[Image:Wheatstonebridge.svg|right|thumb|300px|alt=A Wheatstone bridge has four resistors forming the sides of a diamond shape. A battery is connected across one pair of opposite corners, and a galvanometer across the other pair. |Wheatstone bridge [[circuit diagram]].]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
A '''Wheatstone bridge''' is an electrical circuit used to measure an unknown [[electrical resistance]] by balancing two legs of a [[bridge circuit]], one leg of which includes the unknown component. Its operation is similar to the original [[Potentiometer (measuring instrument)|potentiometer]]. It was invented by [[Samuel Hunter Christie]] in 1833 and improved and popularized by Sir [[Charles Wheatstone]] in 1843.  One of the Wheatstone bridge's initial uses was for the purpose of soils analysis and comparison.<ref>"The Genesis of the Wheatstone Bridge" by Stig Ekelof discusses [[Samuel Hunter Christie|Christie's]] and [[Charles Wheatstone|Wheatstone]]'s contributions, and why the bridge carries Wheatstone's name. Published in "Engineering Science and Education Journal", volume 10, no 1, February 2001, pages 37–40.</ref>


== Operation ==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
In the figure, <math>\scriptstyle R_x</math> is the unknown resistance to be measured; <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math> and <math>\scriptstyle R_3</math> are resistors of known resistance and the resistance of <math>\scriptstyle R_2</math> is adjustable. If the ratio of the two resistances in the known leg <math>\scriptstyle (R_2 / R_1)</math> is equal to the ratio of the two in the unknown leg <math>\scriptstyle (R_x / R_3)</math>, then the [[voltage]] between the two midpoints ('''B''' and '''D''') will be zero and no [[Current (electricity)|current]] will flow through the [[galvanometer]] <math>\scriptstyle V_g</math>. If the bridge is unbalanced, the direction of the current indicates whether <math>\scriptstyle R_2</math> is too high or too low. <math>\scriptstyle R_2</math> is varied until there is no current through the galvanometer, which then reads zero.  
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Detecting zero current with a [[galvanometer]] can be done to extremely high accuracy. Therefore, if <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math> and <math>\scriptstyle R_3</math> are known to high precision, then <math>\scriptstyle R_x</math> can be measured to high precision. Very small changes in <math>\scriptstyle R_x</math> disrupt the balance and are readily detected.
Registered users will be able to choose between the following three rendering modes:


At the point of balance, the ratio of
'''MathML'''
:<math>\begin{align}
:<math forcemathmode="mathml">E=mc^2</math>
  \frac{R_2}{R_1} &= \frac{R_x}{R_3} \\
  \Rightarrow R_x &= \frac{R_2}{R_1} \cdot R_3
\end{align}</math>


Alternatively, if <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math>, and <math>\scriptstyle R_3</math> are known, but <math>\scriptstyle R_2</math> is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of <math>\scriptstyle R_x</math>, using [[Kirchhoff's circuit laws]] (also known as Kirchhoff's rules). This setup is frequently used in [[strain gauge]] and [[resistance thermometer]] measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


==Derivation==
'''source'''
First, [[Kirchoff's first law|Kirchhoff's first rule]] is used to find the currents in junctions '''B''' and '''D''':
:<math forcemathmode="source">E=mc^2</math> -->


:<math>\begin{align}
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
  I_3 - I_x + I_G &= 0 \\
  I_1 - I_2 - I_G &= 0
\end{align}</math>


Then, [[Kirchhoff's circuit laws#Kirchhoff's voltage law (KVL)|Kirchhoff's second rule]] is used for finding the voltage in the loops '''ABD''' and '''BCD''':
==Demos==


:<math>\begin{align}
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
  (I_3 \cdot R_3) - (I_G \cdot R_G) - (I_1 \cdot R_1) &= 0 \\
  (I_x \cdot R_x) - (I_2 \cdot R_2) + (I_G \cdot R_G) &= 0
\end{align}</math>


When the bridge is balanced, then {{math|''I''<sub>''G''</sub> {{=}} 0}}, so the second set of equations can be rewritten as:
:<math>\begin{align}
  I_3 \cdot R_3 &= I_1 \cdot R_1 \\
  I_x \cdot R_x &= I_2 \cdot R_2
\end{align}</math>


Then, the equations are divided and rearranged, giving:
* accessibility:
:<math>R_x = {{R_2 \cdot I_2 \cdot I_3 \cdot R_3}\over{R_1 \cdot I_1 \cdot I_x}}</math>
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


From the first rule, {{math|''I''<sub>''3''</sub> {{=}} ''I''<sub>''x''</sub>}} and {{math|''I''<sub>''1''</sub> {{=}} ''I''<sub>''2''</sub>}}.  The desired value of {{math|''R''<sub>''x''</sub>}} is now known to be given as:
==Test pages ==
:<math>R_x = {{R_3 \cdot R_2}\over{R_1}}</math>


If all four resistor values and the supply voltage ({{math|''V''<sub>''S''</sub>}}) are known, and the resistance of the galvanometer is high enough that {{math|''I''<sub>''G''</sub>}} is negligible, the voltage across the bridge ({{math|''V''<sub>''G''</sub>}}) can be found by working out the voltage from each [[potential divider]] and subtracting one from the other. The equation for this is:
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
:<math>V_G = \left({{R_x}\over{R_3 + R_x}} - {{R_2}\over{R_1 + R_2}}\right)V_s</math>
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


where {{math|''V''<sub>''G''</sub>}} is the voltage of node B relative to node D.
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
== Significance ==
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure [[capacitance]], [[inductance]], [[Electrical impedance|impedance]] and other quantities, such as the amount of combustible gases in a sample, with an [[explosimeter]].  The [[Kelvin bridge]] was specially adapted from the Wheatstone bridge for measuring very low resistances.  In many cases, the significance of measuring the unknown resistance is related to measuring the impact of some physical phenomenon (such as force, temperature, pressure, etc.) which thereby allows the use of Wheatstone bridge in measuring those elements indirectly.
 
The concept was extended to [[alternating current]] measurements by [[James Clerk Maxwell]] in 1865 and further improved by [[Alan Blumlein]] in about 1926.
 
==Modifications of the fundamental bridge==
[[File:Kelvin bridge by RFT.png|right|thumb|300px|[[Kelvin bridge]]]]
The Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are:
* [[Carey Foster bridge]], for measuring small resistances
* [[Kelvin–Varley_divider|Kelvin Varley Slide]]
* [[Kelvin bridge]]
* [[Maxwell bridge]]
 
==See also==
{{Portal|Electronics}}
* [[Murray loop bridge]]
* [[Maxwell bridge]]
* [[Wien bridge]]
* [[Phantom circuit]] - a circuit using a balanced bridge
* [[Post Office Box (electricity)|Post Office Box]]
* [[Potentiometer]]
* [[Potential divider]]
* [[Ohmmeter]]
* [[Resistance thermometer]]
* [[Strain gauge]]
* [[E-meter]] - a variation used by [[Scientology]]
 
==References==
<references/>
 
==External links==
* [http://www.magnet.fsu.edu/education/tutorials/java/wheatstonebridge/index.html Wheatstone Bridge - Interactive Java Tutorial] National High Magnetic Field Laboratory
*[http://www.efunda.com/designstandards/sensors/methods/wheatstone_bridge.cfm efunda Wheatstone article]
*[http://books.google.com/books?id=z3lKAAAAMAAJ Methods of Measuring Electrical Resistance - Edwin F. Northrup, 1912, full-text on Google Books]
*[http://www.strainmatics.com Measuring strain using Wheatstone bridge principles]
 
{{DEFAULTSORT:Wheatstone Bridge}}
[[Category:Electrical meters]]
[[Category:Electrical circuits]]
[[Category:Measuring instruments]]
[[Category:English inventions]]
[[Category:Impedance measurements]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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