Carey Foster bridge

In electronics, the Carey Foster bridge is a bridge circuit used to measure medium resistances, or to measure small differences between two large resistances. It was invented by Carey Foster as a variant on the Wheatstone bridge. 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 adjacent diagram, 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 busbars of very low resistance, to limit the influence on the measurement.

# Place a known resistance in position Y.
# Place the unknown resistance in position X.
# Adjust the contact D along the bridge wire EF so as to null the galvanometer. This position (as a percentage of distance from E to F) is .
# Swap X and Y. Adjust D to the new null point. This position is .
# If the resistance of the wire per percentage is , then the resistance difference is the resistance of the length of bridge wire between and :

::: $X-Y=\sigma(\ell_2-\ell_1) \,$

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, when the bridge is unbalanced, the galvanometer is shunted with a low resistance to avoid burning it out. It is only used at full sensitivity when the anticipated
measurement is 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) that is 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:

:$+ 1 =$       ''(equation 1)''

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

:$=$

and add 1 to each side:

:$+ 1 =$       ''(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:

:$\begin &Y + \sigma(100 - \ell_1 + \beta) = X + \sigma (100 - \ell_2 + \beta) \\ \Rightarrow &X - Y = \sigma(\ell_2 - \ell_1) \end$

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.

References

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{{Bridge circuits

Analog circuits
Bridge circuits
English inventions
Impedance measurements