Wheatstone bridge: Definition from Answers.com

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.

1 The bridge's operation
2 Derivation
3 Significance
4 Modification of the fundamental bridge
5 See also
6 External links

The bridge's operation

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 $(R 2 / R 1)$ 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 $V g$ . $R 2$ is varied until this condition is reached. The direction of the current 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, $R_x = (R_2 / R_1) \cdot R_3$

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, 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:

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

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 double bridge was specially adapted from the Wheatstone bridge for measuring very low resistances.

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

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

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Donate to Wikimedia

		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Electronics Dictionary. Copyright 2001 by Twysted Pair. All rights reserved. Read more
		WordNet. WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. Read more
		Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Wheatstone bridge". Read more

	acoustic bridge (electronics)
	balanced bridge (electricity)
	Kohlrausch method (physical chemistry)

	How do you reduce power consumption of a Wheatstone Bridge without changing the bridge resistances? Read answer...
	Advantages and disadvantages of wheatstone bridge? Read answer...
	Explain the advantages of the wheatstone bridge method of measuring resistance? Read answer...

	Why Meter bridge is more sensitive then post office box as both are based on wheatstone bridge principle?
	Limitation of wheatstone bridge?
	Where in the car is a wheatstone bridge?

Wheatstone bridge

Contents

The bridge's operation

Derivation

Significance

Modification of the fundamental bridge

See also

External links