Wheatstone bridge

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Wheat·stone bridge

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Wheatstone bridge

to calculate the unknown resistance: R
= (

) R
(Academy Artworks)

(hwēt'stōn', wēt'-) pronunciation

also Wheat·stone's bridge (-stōnz')
n.
An instrument or a circuit consisting of four resistors or their equivalent in series, used to determine the value of an unknown resistance when the other three resistances are known.

[After Sir Charles Wheatstone (1802-1875), British physicist and inventor.]

Wheatstone bridge

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A device used to measure the electrical resistance of an unknown resistor by comparing it with a known standard resistance. This method was first described by S. H. Christie in 1833. Since 1843 when Sir Charles Wheatstone called attention to Christie's work, Wheatstone's name has been associated with this network.

Wheatstone bridge circuit.

The Wheatstone bridge network consists of four resistors R_AB, R_BC, R_CD, and R_AD interconnected as shown in the illustration to form the bridge. A detector G, having an internal resistance R_G, is connected between the B and D bridge points; and a power supply, having an open-circuit voltage E and internal resistance R_B, is connected between the A and C bridge points. See also Bridge circuit.

If the network is adjusted so that Eq. (1) is satisfied, the
1. $R_{BC}R_{AD} - R_{AB}R_{CD} = 0$
detector current will be zero and this adjustment will be independent of the supply voltage, the supply resistance, and the detector resistance. Thus, when the bridge is balanced, Eq. (2)
2. $R_{BC}R_{AD} = R_{AB}R_{CD}$
holds, and, if it is assumed that the unknown resistance is the one in the CD arm of the bridge, then it is given by Eq. (3).
3. $R_{CD} =\left({R_{BC}\over R_{AB}}\right)\times R_{AD}$
See also Resistance measurement.

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wheatstone bridge

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Four arm bridge circuit used to measure resistance, inductance or capacitance.

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Electricity and Electronics - Wheatstone bridge: test instrument that joins two branches of circuit to measure resistance by comparing it with a known resistance

Wikipedia on Answers.com:

Wheatstone bridge

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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.

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. 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. ^[1]

Contents

1 Operation
2 Derivation
3 Significance
4 Modifications of the fundamental bridge
5 See also
6 References
7 External links

Operation

In the figure, $R_x$ 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 $(R_2 / R_1)$ is equal to the ratio of the two in the unknown leg $(R_x / R_3)$ , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer $V_g$ . If the bridge is unbalanced, the direction of the current indicates whether $R_2$ is too high or too low. $R_2$ is varied until there is no current through the galvanometer, which then reads zero.

Detecting zero current with a galvanometer can be done to extremely high accuracy. 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, $R_x = (R_2 / R_1) \cdot R_3$

Alternatively, if $R_1$ , $R_2$ , and $R_3$ are known, but $R_2$ is not adjustable, the voltage difference across 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 thermometer 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:

$I_3 \ - I_x \ + I_G = 0$

$I_1 \ - I_2 \ - I_G = 0$

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

$(I_3 \cdot R_3) - (I_G \cdot R_G) - (I_1 \cdot R_1) = 0$

$(I_x \cdot R_x) - (I_2 \cdot R_2) + (I_G \cdot R_G) = 0$

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, and the resistance of the galvanometer is high enough that $I_G$ is negligible, the voltage across the bridge ( $V_G$ ) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:

$V_G = {{R_x}\over{R_3 + R_x}}V_s - {{R_2}\over{R_1 + R_2}}V_s$

This can be simplified to:

$V_G = \left({{R_x}\over{R_3 + R_x}} - {{R_2}\over{R_1 + R_2}}\right)V_s$

where $V_G$ is the voltage of node B relative to node D.

Significance

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 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

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 Slide
Kelvin bridge
Maxwell bridge

References

^ "The Genesis of the Wheatstone Bridge" by Stig Ekelof discusses Christie's and 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.

External links

Wheatstone Bridge - Interactive Java Tutorial National High Magnetic Field Laboratory
efunda Wheatstone article
Methods of Measuring Electrical Resistance - Edwin F. Northrup, 1912, full-text on Google Books
Measuring strain using Wheatstone bridge principles

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American Heritage Dictionary The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved. Read

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Wheatstone bridge

Wheat·stone bridge

Wheatstone bridge

wheatstone bridge

categories related to 'Wheatstone bridge'

Wheatstone bridge

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Derivation

Significance

Modifications of the fundamental bridge

See also

References

External links

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