Wheatstone bridge

Wheatstone's bridge circuit diagram.

A Wheatstone bridge is an electrical circuit 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.

what are name of Wheatstone bridge resistences

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

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 Double bridge
• Maxwell bridge

See also

• Murray loop bridge
• Maxwell bridge
• Wein's bridge, see Wien bridge
• Phantom circuit - a circuit using a balanced bridge
• Post Office Box
• Potentiometer
• Potential divider
• Ohmmeter
• Resistance thermometer
• Strain gauge

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