Fig. 564.--Diagram showing principle of Wheatstone's bridge. A, B, C, and D, are the four members which constitute the bridge. The current from the battery divides at P, part traversing DC, and part traversing BA. The galvanometer connected to M and N will indicate when the currents are equal in the two branches by giving no deflection. This is then a zero or nil method of testing. The resistances and keys required in testing are shown in [fig. 565]. In the actual instrument, the members A, B, C, and D are known by the names given in the figure.
Wheatstone Bridge Method.--For accurate measurements of resistance this method is almost universally used. The so-called "Wheatstone" bridge was invented by Christie, and improperly credited to Wheatstone, who simply applied Christie's invention to the measurement of resistances.
Fig. 565.--Diagram showing arms of Wheatstone bridge, resistances and method of connecting galvanometer, battery and unknown resistance.
The bridge consists of a system of conductors as shown in [fig. 564]. The circuit of a constant battery is made to branch at P into two parts, which re-unite at Q, so that part of the current flows through the point M, the other part through the point N. The four conductors A, B, C, D, are spoken of as the arms of the balance or bridge. It is by the proportion existing between the resistances of these arms that the resistance of one of them can be calculated when the resistances of the other three are known. When the current which starts from the battery arrives at P, the pressure will have fallen to a certain value. The pressure in the upper branch falls again to M, and continues to fall to Q. The pressure of the lower branch falls to N, and again falls till it reaches the value at Q. Now if N be the same proportionate distance along the resistances between P and Q, as M is along the resistances of the upper line between P and Q, the pressure will have fallen at N to the same value as it has fallen to at M; or, in other words, if the ratio of the resistance C to the resistance D be equal to the ratio between the resistance A and the resistance B, then M and N will be at equal pressures. To find out if this condition obtain, a sensitive galvanometer is placed in a branch wire between M and N which will show no deflection when M and N are at equal pressure or when the four resistances of the arms "balance" one another by being in proportion, thus:
(1) A:C = B:D
If, then, the value of A, B, and C be known, D can be calculated. The proportion (1) is reduced to the following equation before substituting.
D = BC/A