Science Education Mini-Lesson: The Bridge Method (for measuring electrical resistance)

Single-arm bridge: The principle is shown in the figure. In the figure, R₁ and R₂ are standard resistors, and R₃ is a variable resistor. Adjust R3 to balance the bridge, so that the current flowing through the galvanometer I_G = 0, i.e., U_A = U_B. At this time, I₂ = I₃, I_X = I₁, I₃R₃ = I_XR_X, and I₂R₂ = I₁R₁.  Therefore, R_X = R₁/R₂ * R₃.

In practice, due to the resistance of the connecting wires to R_X, the single-arm bridge cannot be used for measuring small resistances.  Furthermore, the regulations stipulate that the connecting wire resistance should not exceed 0.2% of the measured resistance value; if it exceeds this value, correction is required.

There are many models of single-arm bridges, such as QJ-23, QJ-24, QJ-49, QJ-57, and QJ-67, with a measurement range of 1-10⁸Ω and accuracies of 0.2, 0.1, and 0.05/0.01 levels. The figure shows the appearance of several DC single-arm bridges.

Double-Arm Bridge: Single-arm bridges are only suitable for measuring DC resistances greater than 1Ω. For measuring DC resistances less than 1Ω, a double-arm bridge can be used, the principle of which is shown in the figure.

In the figure, the measured resistance R_X and the standard resistance R_N are connected using a four-terminal connection. C1, C2, C3, and C4 are current terminals, and P1, P2, P3, and P4 are voltage terminals.

When the bridge is balanced, I_G=0, I₁=I₂, I₃=I₄, I₁R=IR_X+I₃R’, I₂R₁=IR_N+I₄R₂, R=R’, R₁=R₂, R_X=R/R₁*R_N.  There are many models of double-arm bridges, such as QJ-42, QJ-44, QJ-19, and QJ-65, with a measurement range of 10⁻⁶ to 11Ω and accuracies of 0.2, 0.05, and 0.02 grades. 

Single and Double Arm Bridges

These bridges combine the functions of both single-arm and double-arm bridges, offering a wide measurement range, typically between 10⁻⁶ and 10⁷ Ω.  Examples include the QJ-31, QJ32, QJ36, and QJ47 models, with accuracies of 0.1, 0.05, and 0.02 levels, as shown in the figures below, which illustrate the external appearance of several types of DC single and double arm bridges.