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A Wheatstone bridge is an electrical circuit used to measure an unknown
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...
by balancing two legs of a
bridge circuit A bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge ...
, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to provide extremely accurate measurements (in contrast with something like a simple voltage divider). Its operation is similar to the original potentiometer. The Wheatstone bridge was invented by Samuel Hunter Christie (sometimes spelled "Christy") in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. One of the Wheatstone bridge's initial uses was for
soil analysis Soil test may refer to one or more of a wide variety of soil analysis conducted for one of several possible reasons. Possibly the most widely conducted soil tests are those done to estimate the plant-available concentrations of plant nutrients, i ...
and comparison."The Genesis of the Wheatstone Bridge" by Stig Ekelof discusses
Christie's Christie's is a British auction house founded in 1766 by James Christie. Its main premises are on King Street, St James's in London, at Rockefeller Center in New York City and at Alexandra House in Hong Kong. It is owned by Groupe Artémi ...
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.


Operation

In the figure, is the fixed, yet unknown, resistance to be measured. and are resistors of known resistance and the resistance of is adjustable. The resistance is adjusted until the bridge is "balanced" and no current flows through the galvanometer . At this point, the potential difference between the two midpoints (B and D) will be zero. Therefore the ratio of the two resistances in the known leg is equal to the ratio of the two resistances in the unknown leg . If the bridge is unbalanced, the direction of the current indicates whether is too high or too low. At the point of balance, :\begin \frac &= \frac \\ pt \Rightarrow R_x &= \frac \cdot R_3 \end Detecting zero current with a galvanometer can be done to extremely high precision. Therefore, if and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected. Alternatively, if and are known, but is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of using Kirchhoff's circuit laws. This setup is frequently used in
strain gauge A strain gauge (also spelled strain gage) is a device used to measure strain on an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports ...
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


Quick derivation at balance

At the point of balance, both the
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
and the current between the two midpoints (B and D) are zero. Therefore, I_1 = I_2 , I_3 = I_x , V_D = V_B , and: \begin \frac&=\frac \\ pt \Rightarrow \frac &= \frac\\ pt \Rightarrow R_x &= \frac \cdot R_3 \end


Full derivation using Kirchhoff's circuit laws

First, Kirchhoff's first law is used to find the currents in junctions B and D: :\begin I_3 - I_x + I_G &= 0 \\ I_1 - I_2 - I_G &= 0 \end Then, Kirchhoff's second law is used for finding the voltage in the loops ABDA and BCDB: :\begin (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 When the bridge is balanced, then , so the second set of equations can be rewritten as: :\begin I_3 \cdot R_3 &= I_1 \cdot R_1 \quad \text \\ I_x \cdot R_x &= I_2 \cdot R_2 \quad \text \end Then, equation (1) is divided by equation (2) and the resulting equation is rearranged, giving: :R_x = Due to and being proportional from Kirchhoff's First Law, cancels out of the above equation. The desired value of is now known to be given as: :R_x = On the other hand, if the resistance of the galvanometer is high enough that is negligible, it is possible to compute from the three other resistor values and the supply voltage (), or the supply voltage from all four resistor values. To do so, one has to work out the voltage from each
potential divider In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distributing the inp ...
and subtract one from the other. The equations for this are: : \begin V_G & = \left( - \right)V_s \\ ptR_x & = R_3 \end where 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 Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
,
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of th ...
, 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 A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfrie ...
(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 Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
measurements by
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
in 1865 and further improved as by Alan Blumlein in British Patent no. 323,037, 1928.


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: * Carey Foster bridge, for measuring small resistances * Kelvin bridge, for measuring small four-terminal resistances *
Maxwell bridge A Maxwell bridge is a modification to a Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and inductance or resistance and capacitance. When the calibrated components are a paral ...
, and Wien bridge for measuring reactive components * Anderson's bridge, for measuring the self-inductance of the circuit, an advanced form of Maxwell’s bridge


See also

* Diode bridge, product mixer – diode bridges * Phantom circuit – a circuit using a balanced bridge * Post office box (electricity) * Potentiometer (measuring instrument) *
Potential divider In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distributing the inp ...
* Ohmmeter * Resistance thermometer *
Strain gauge A strain gauge (also spelled strain gage) is a device used to measure strain on an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports ...


References


External links

*
''DC Metering Circuits''
chapter fro

free ebook an
''Lessons In Electric Circuits''
series.
Test Set I-49
{{DEFAULTSORT:Wheatstone Bridge Electrical meters Bridge circuits Measuring instruments English inventions Impedance measurements pl:Mostek (elektronika)#Mostek Wheatstone'a