World Library  
Flag as Inappropriate
Email this Article

Wheatstone bridge

Article Id: WHEBN0000033894
Reproduction Date:

Title: Wheatstone bridge  
Author: World Heritage Encyclopedia
Language: English
Subject: Carey Foster bridge, Strain gauge, Bolometer, Loadpin, Catalytic bead sensor
Collection: Bridge Circuits, Electrical Meters, English Inventions, Impedance Measurements, Measuring Instruments
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Wheatstone bridge

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

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

Operation

In the figure, \scriptstyle R_x is the unknown resistance to be measured; \scriptstyle R_1, \scriptstyle R_2 and \scriptstyle R_3 are resistors of known resistance and the resistance of \scriptstyle R_2 is adjustable. If the ratio of the two resistances in the known leg \scriptstyle (R_2 / R_1) is equal to the ratio of the two in the unknown leg \scriptstyle (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 \scriptstyle V_g. If the bridge is unbalanced, the direction of the current indicates whether \scriptstyle R_2 is too high or too low. \scriptstyle 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 \scriptstyle R_1, \scriptstyle R_2 and \scriptstyle R_3 are known to high precision, then \scriptstyle R_x can be measured to high precision. Very small changes in \scriptstyle R_x disrupt the balance and are readily detected.

At the point of balance, the ratio of

\begin{align} \frac{R_2}{R_1} &= \frac{R_x}{R_3} \\ \Rightarrow R_x &= \frac{R_2}{R_1} \cdot R_3 \end{align}

Alternatively, if \scriptstyle R_1, \scriptstyle R_2, and \scriptstyle R_3 are known, but \scriptstyle R_2 is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of \scriptstyle 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

Directions of currents arbitrarily assigned

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

\begin{align} I_3 - I_x + I_G &= 0 \\ I_1 - I_2 - I_G &= 0 \end{align}

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

\begin{align} (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}

When the bridge is balanced, then IG = 0, so the second set of equations can be rewritten as:

\begin{align} I_3 \cdot R_3 &= I_1 \cdot R_1 \\ I_x \cdot R_x &= I_2 \cdot R_2 \end{align}

Then, the equations are divided and rearranged, giving:

R_x =

From the first rule, I3 = Ix and I1 = I2. The desired value of Rx is now known to be given as:

R_x =

If all four resistor values and the supply voltage (VS) are known, and the resistance of the galvanometer is high enough that IG is negligible, the voltage across the bridge (VG) 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 = \left( - \right)V_s

where VG is the voltage of node D relative to node B.

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 around 1926.

Modifications 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:

See also

References

  1. ^ "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
  • Measuring strain using Wheatstone bridge principles
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.