Wheatstone's Balance.—The electrical conductivity of a body is determined by ascertaining the ratio between the resistance of a certain length of the conductor in question, having a given section, to that of a known length of a known section of some substance taken as a standard.
For this purpose Wheatstone's bridge in connection with a box of resistance coils is the most convenient method.
At [Fig. 94] is shown Wheatstone's balance (Post-office pattern), and at [Fig. 93] the apparatus is reduced into the form of a parallelogram, which is the usual diagram of Wheatstone's bridge. The theory of the bridge is as follows:
Four conductors A B, B C, A D, and D C are joined at A and C to the poles of a battery Z; the resistance between A and B is R; that between A and D is r; that between D and C is R1; and that between B and C is x, the unknown resistance to be measured. A convenient constant ratio is chosen for R1 and r, such as equality 1 to 10, 1 to 100, or 1 to 1000; and then R1 is adjusted until no current flows through the galvanometer G; when this is the case we have R : r=R1 : x, or x = (r/R) × R1; so that if r = R/100, x will be equal to R1/100.
Two keys a and b are inserted; the current is wholly cut off the four conductors until contact is made at a; and then after the currents in the four conductors have come to their permanent condition, contact is made at b to test whether any current flows through the galvanometer. The three resistances R, R1 and r and the resistance of the galvanometer should be small if x is small, and great if x is great.
The conductors A B and A D of the bridge are each formed of three resistance coils having a resistance of 10, 100, and 1000 ohms respectively, inserted between the terminals B and D of the balance, [Fig. 94].
The conductor D C is formed of a set of resistance coils from 1 up to 4000 ohms, amounting altogether to 11,110 ohms, inserted between the terminals D and C of the balance; in the balance, a brass plug being inserted between the terminals D and D1, they may be considered as one terminal D. The conductor B C is the wire to be tested, and is connected to the terminals B and C of the balance.
Measurement of Resistances.—When a resistance is to be measured that is within the range of the coils in R1, R and r are made equal. The needle of the galvanometer will move in a different direction, either to the right or to the left, according as the resistance in R1 is greater or less than the line wire x. The needle remains at zero only when the resistance in R1 is equal to that in x. For r : R :: R1 : x.
WHEATSTONE'S BRIDGE.