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# Wheatstone bridge

A Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is 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 except that in potentiometer circuits the meter used is a sensitive galvanometer.

In the circuit on the right, $R_x$ is the unknown resistance to be measured; $R_1$, $R_2$ and $R_3$ are resistors of known resistance and the resistance of $R_2$ is adjustable. If the ratio of the two resistances in the known leg $\left(R_2 / R_1\right)$ is equal to the ratio of the two in the unknown leg $\left(R_x / R_3\right)$, then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer $V_g$. $R_2$ is varied until this condition is reached. The current direction indicates whether $R_2$ is too high or too low.

Detecting zero current can be done to extremely high accuracy (see galvanometer). Therefore, if $R_1$, $R_2$ and $R_3$ are known to high precision, then $R_x$ can be measured to high precision. Very small changes in $R_x$ disrupt the balance and are readily detected.

At the point of balance, the ratio of $R_2 / R_1 = R_x / R_3$

Therefore, $R_x = \left(R_2 / R_1\right) cdot R_3$

Alternatively, if $R_1$, $R_2$, and $R_3$ are known, but $R_2$ is not adjustable, the voltage or current flow through the meter can be used to calculate the value of $R_x$, using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is frequently used in strain gauge and Resistance Temperature Detector measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

Derivation

First, Kirchhoff's first rule is used to find the currents in junctions B and D:::

:$I_3 - I_x + I_g = 0$:$I_1 - I_g - I_2 = 0$

Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:

:$\left(I_3 cdot R_3\right) - \left(I_g cdot R_g\right) - \left(I_1 cdot R_1\right) = 0$:$\left(I_x cdot R_x\right) - \left(I_2 cdot R_2\right) + \left(I_g cdot R_g\right) = 0$

The bridge is balanced and $I_g = 0$, so the second set of equations can be rewritten as::$I_3 cdot R_3 = I_1 cdot R_1$:$I_x cdot R_x = I_2 cdot R_2$

Then, the equations are divided and rearranged, giving::$R_x =$R_2 cdot I_2 cdot I_3 cdot R_3}over{R_1 cdot I_1 cdot I_x

From the first rule, $I_3 = I_x$ and $I_1 = I_2$. The desired value of $R_x$ is now known to be given as::$R_x =$R_3 cdot R_2}over{R_1

If all four resistor values and the supply voltage ($V_s$) are known, the voltage across the bridge ($V$) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:

:$V =$R_x}over{R_3 + R_xV_s - R_2}over{R_1 + R_2V_s

This can be simplified to:

:$V = left\left($R_x}over{R_3 + R_x - R_2}over{R_1 + R_2 ight)V_s

ignificance

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, impedance and other quantities, such as the amount of combustible gases in a sample, with an explosimeter. The Kelvin double bridge was specially adapted from the Wheatstone bridge for measuring very low resistances. A "Kelvin one-quarter bridge" has also been developed. It has been theorized that a "three-quarter bridge" could exist; however, such a bridge would function identically to the Kelvin double bridge.

The concept was extended to alternating current measurements by James Clerk Maxwell in 1865 and further improved by Alan Blumlein in about 1926.

Modification of the fundamental 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:
* Karey-Foster Slide-wire bridge
* Kelvin Varley Slide
* Kelvin Double bridge
* Maxwell bridge

* Strain gauge
* Potentiometer
* Potential divider
* Ohmmeter
* Resistance Temperature Detector
* Maxwell bridge

* [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]

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### Look at other dictionaries:

• Wheatstone bridge — [hwēt′stōn΄, wēt′stōn΄; ] chiefly Brit [, wēt′stən, hwēt′stən] n. [after Sir Charles Wheatstone (1802 75), Eng physicist] 1. a divided bridge circuit (see BRIDGE1, n. 11) having four resistances in series, used to find the value of an unknown… …   English World dictionary

• Wheatstone bridge — Wheat·stone bridge .hwēt .stōn , .wēt , chiefly Brit stən n a bridge for measuring electrical resistances that consists of a conductor joining two branches of a circuit Wheatstone Sir Charles (1802 1875) British physicist. Wheatstone was… …   Medical dictionary

• Wheatstone bridge — Vitstono tiltelis statusas T sritis fizika atitikmenys: angl. Wheatstone bridge vok. Wheatstone Brücke, f rus. мост Уитстона, m pranc. pont Wheatstone, m …   Fizikos terminų žodynas

• Wheatstone bridge — Vitstono tiltelis statusas T sritis chemija apibrėžtis Įrenginys elektriniams parametrams matuoti kompensavimo būdu. atitikmenys: angl. Wheatstone bridge rus. мостик Уитстона …   Chemijos terminų aiškinamasis žodynas

• wheatstone bridge — bridge used to measure electrical resistances …   English contemporary dictionary

• Wheatstone bridge — Elect. a circuit for measuring an unknown resistance by comparing it with known resistances. Also, Wheatstone s bridge. Cf. bridge (def. 9), null method. [1870 75; named after C. WHEATSTONE] * * * …   Universalium

• Wheatstone bridge — /ˌwitstən ˈbrɪdʒ/ (say .weetstuhn brij) noun an instrument designed for measuring the electrical resistance of a circuit or a circuit component. Also, Wheatstone s bridge. {named after Sir Charles Wheatstone, 1802–75, English physicist and… …   Australian English dictionary

• Wheatstone bridge — noun Etymology: Sir Charles Wheatstone Date: 1872 an electrical bridge consisting of two branches of a parallel circuit joined by a galvanometer and used for determining the value of an unknown resistance in one of the branches …   New Collegiate Dictionary

• Wheatstone bridge — Wheat′stone bridge n. elm an electrical circuit that measures resistance comparatively • Etymology: 1870–75; after C. Wheatstone …   From formal English to slang

• Wheatstone bridge — noun a device for measuring an unknown resistance by combining it with a known resistance and comparing the ratio of the two with another pair of resistances of known ratio. Origin C19: named after the English physicist Sir Charles Wheatstone …   English new terms dictionary