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A Wheatstone bridge is a measuring instrument
Measuring instrument

In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantity of real-world object and phenomenon....
 invented by Samuel Hunter Christie
Samuel Hunter Christie

Samuel Hunter Christie was a British scientist and mathematician. He studied mathematics at Trinity College, Cambridge. He was particularly interested in magnetism, studying the earth's magnetic field and designing improvements to the magnetic compass....
 in 1833 and improved and popularized by Sir Charles Wheatstone
Charles Wheatstone

Knighthood Charles Wheatstone Fellow of the Royal Society , was a United Kingdom scientist and inventor of many scientific breakthroughs of the Victorian era, including the English concertina, the stereoscope , and the Playfair cipher ....
 in 1843. It is used to measure an unknown electrical resistance
Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
 by balancing two legs of a bridge circuit
Bridge circuit

A bridge circuit is a type of electrical circuit in which the Current in a conductor splits into two parallel paths and then recombines into a single conductor, thereby enclosing a loop....
, one leg of which includes the unknown component. Its operation is similar to the original potentiometer
Potentiometer (measuring instrument)

A potentiometer is an instrument for measuring the potential in a circuit taps off a fraction of a known voltage from a resistive slide wire and compares it with the unknown voltage by means of a galvanometer....
 except that in potentiometer circuits the meter used is a sensitive galvanometer
Galvanometer

A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an Analogue electronics electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil....
.

In the circuit on the right, is the unknown resistance to be measured; , and are resistors of known resistance and the resistance of is adjustable.






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Encyclopedia


A Wheatstone bridge is a measuring instrument
Measuring instrument

In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantity of real-world object and phenomenon....
 invented by Samuel Hunter Christie
Samuel Hunter Christie

Samuel Hunter Christie was a British scientist and mathematician. He studied mathematics at Trinity College, Cambridge. He was particularly interested in magnetism, studying the earth's magnetic field and designing improvements to the magnetic compass....
 in 1833 and improved and popularized by Sir Charles Wheatstone
Charles Wheatstone

Knighthood Charles Wheatstone Fellow of the Royal Society , was a United Kingdom scientist and inventor of many scientific breakthroughs of the Victorian era, including the English concertina, the stereoscope , and the Playfair cipher ....
 in 1843. It is used to measure an unknown electrical resistance
Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
 by balancing two legs of a bridge circuit
Bridge circuit

A bridge circuit is a type of electrical circuit in which the Current in a conductor splits into two parallel paths and then recombines into a single conductor, thereby enclosing a loop....
, one leg of which includes the unknown component. Its operation is similar to the original potentiometer
Potentiometer (measuring instrument)

A potentiometer is an instrument for measuring the potential in a circuit taps off a fraction of a known voltage from a resistive slide wire and compares it with the unknown voltage by means of a galvanometer....
 except that in potentiometer circuits the meter used is a sensitive galvanometer
Galvanometer

A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an Analogue electronics electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil....
.

In the circuit on the right, is the unknown resistance to be measured; , and are resistors of known resistance and the resistance of is adjustable. If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg , then the voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
 between the two midpoints (B and D) will be zero and no current will flow through the galvanometer
Galvanometer

A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an Analogue electronics electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil....
 . is varied until this condition is reached. The current direction indicates whether is too high or too low.

Detecting zero current can be done to extremely high accuracy (see galvanometer
Galvanometer

A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an Analogue electronics electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil....
). 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.

At the point of balance, the ratio of

Therefore,

Alternatively, if , , and are known, but is not adjustable, the voltage or current flow through the meter can be used to calculate the value of , using Kirchhoff's circuit laws
Kirchhoff's circuit laws

Kirchhoff's circuit laws are two Equality that deal with the Charge conservation and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff....
 (also known as Kirchhoff's rules). This setup is frequently used in strain gauge
Strain gauge

A strain gauge is a device used to measure the Strain of an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an Electrical insulation flexible backing which supports a metallic foil pattern....
 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:


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

The bridge is balanced and , so the second set of equations can be rewritten as:

Then, the equations are divided and rearranged, giving:

From the first rule, and . The desired value of is now known to be given as:

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

This can be simplified to:

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

In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge.Capacitance is also a measure of the amount of electric charge stored for a given electric potential....
, inductance
Inductance

Inductance is the property in an electrical circuit where a change in the current flowing through that circuit induces an Electromotive force that opposes the change in current ....
, impedance
Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of Electrical resistance to AC circuits, describing not only the relative amplitudes of the voltage and Electric current, but also the relative Phase ....
 and other quantities, such as the amount of combustible gases in a sample, with an explosimeter
Explosimeter

An explosimeter is a device which is used to measure the amount of combustible gases present in a sample. When a percentage of the lower explosive limit of an atmosphere is exceeded, an alarm signal on the instrument is activated....
. The Kelvin double bridge was specially adapted from the Wheatstone bridge for measuring very low resistances.

The concept was extended to alternating current
Alternating current

In alternating current the movement of electric charge periodically reverses direction. An electric charge would for instance move forward, then backward, then forward, then backward, over and over again....
 measurements by James Clerk Maxwell
James Clerk Maxwell

James Clerk Maxwell was a Scotland Mathematical physics. His most significant achievement was the development of the classical electromagnetic theory, synthesizing all previous unrelated observations, experiments and equations of electricity, magnetism and even optics into a consistent theory....
 in 1865 and further improved by Alan Blumlein
Alan Blumlein

Alan Dower Blumlein was an electronics engineer who made many inventions in telecommunications, sound recording, stereophonic sound, television and radar....
 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
    Maxwell bridge

    |- align = "center"||width = "25"|| A Maxwell bridge is a type of Wheatstone bridge used to measure an unknown inductance in terms of calibrated Electrical resistance and capacitance....


See also


  • Maxwell bridge
    Maxwell bridge

    |- align = "center"||width = "25"|| A Maxwell bridge is a type of Wheatstone bridge used to measure an unknown inductance in terms of calibrated Electrical resistance and capacitance....
  • Phantom circuit
    Phantom circuit

    In telecommunication and electrical engineering, a phantom circuit is an electrical circuit derived from suitably arranged wires with one or more conductive paths being a circuit in itself and at the same time acting as one conductor of another circuit....
     - a circuit using a balanced bridge
  • Post Office Box
    Post Office Box (electricity)

    The Post Office Box was a wheatstone bridge style testing device with pegs and spring arms to close electrical circuits and measure properties of the circuit under test....
  • Potentiometer
    Potentiometer

    A potentiometer is a three-terminal resistor with a sliding contact that forms an adjustable voltage divider. If only two terminals are used , it acts as a variable resistor or Rheostat....
  • Potential divider
  • Ohmmeter
    Ohmmeter

    An ohmmeter is an electricity measuring instrument that measures electrical resistance, the opposition to an electric current. Micro-ohmmeters make low resistance measurements....
  • Resistance Temperature Detector
  • Strain gauge
    Strain gauge

    A strain gauge is a device used to measure the Strain of an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an Electrical insulation flexible backing which supports a metallic foil pattern....


External links

  • National High Magnetic Field Laboratory