In electronics

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, the Carey Foster bridge is a bridge circuit

Bridge circuit

A bridge circuit is a type of electrical circuit in which two circuit branches are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge was originally developed for laboratory measurement purposes and one of the intermediate...

 used to measure low resistances, or to measure small differences between two large resistances. It was invented by Carey Foster

Carey Foster

George Carey Foster was a chemist and physicist, born at Sabden in Lancashire,He was Professor of Physics at University College London.-Early life:...

 as a variant on the Wheatstone bridge

Wheatstone bridge

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...

. He first described it in his 1872 paper "On a Modified Form of Wheatstone's Bridge, and Methods of Measuring Small Resistances" (Telegraph Engineer's Journal, 1872-1873, 1, 196).

Use

In the diagram to the right, X and Y are resistances to be compared. P and Q are nearly equal resistances, forming the other half of the bridge. The bridge wire EF has a jockey contact D placed along it and is slid until the galvanometer G measures zero. The thick-bordered areas are thick copper busbar

Busbar

In electrical power distribution, a bus bar is a strip of copper or aluminium that conducts electricity within a switchboard, distribution board, substation or other electrical apparatus....

s of almost zero resistance.

1. Place a known resistance R in position Y.
2. Place the unknown resistance in position X.
3. Place D along the bridge wire EF such as to null the galvanometer. This position (as a percentage of distance from E to F) is .
4. Swap X and Y. Place D at the new null point. This position is .
5. If the resistance of the wire per percentage is , then the resistance difference is the resistance of the length of bridge wire between and :

To measure a low unknown resistance X, replace Y with a copper busbar that can be assumed to be of zero resistance.

In practical use, shunt the galvanometer with a low resistance when the bridge is unbalanced, to avoid burning it out. Only use at full sensitivity when you are close to the null point.

To measure σ

To measure the unit resistance of the bridge wire EF, put a known resistance (e.g. a standard 1 ohm resistance) less than that of the wire as X and a copper busbar of assumed zero resistance as Y.

Theory

Two resistances to be compared, X and Y, are connected in series with the bridge wire. Thus, considered as a Wheatstone bridge, the two resistances are X plus a length of bridge wire, and Y plus the remaining bridge wire. The two remaining arms are the nearly equal resistances P and Q, connected in the inner gaps of the bridge.
Let be the null point D on the bridge wire EF in percent. is the unknown left-side extra resistance EX and is the unknown right-side extra resistance FY, and is the resistance per percent length of the bridge wire:


and add 1 to each side:
      (equation 1)

Now swap X and Y. is the new null point reading in percent:


and add 1 to each side:
      (equation 2)

Equations 1 and 2 have the same left-hand side and the same numerator on the right-hand side, meaning the denominator on the right-hand side must also be equal:

Thus: the difference between X and Y is the resistance of the bridge wire between and .

The bridge is most sensitive when P, Q, X and Y are all of comparable magnitude.