A Wheatstone bridge circuit is an accurate device for measuring resistance. This circuit, shown in Fig. 2.47, is used to measure the unknown resistor R_{x}. The center leg of the circuit contains a galvanometer, which is a very sensitive device that can be used to measure current in the microamp range. When the unknown resistor is connected to the bridge, R_{3} is adjusted until the current in the galvanometer is zero, at which point the bridge is balanced. In this balanced condition
\frac{R_{1}}{R_{3}}\,=\,\frac{R_{2}}{R_{x}}
so that
R_{x}\,=\,\left(\frac{R_{2}}{R_{1}}\right)R_{3}
Engineers also use this bridge circuit to measure strain in solid material. For example, a system used to determine the weight of a truck is shown in Fig. 2.48a. The platform is supported by cylinders on which strain gauges are mounted. The strain gauges, which measure strain when the cylinder deflects under load, are connected to a Wheatstone bridge as shown in Fig. 2.48b. The strain gauge has a resistance of 120 Ω under no-load conditions and
changes value under load. The variable resistor in the bridge is a calibrated precision device. Weight is determined in the following manner. The ΔR_{3} required to balance the bridge represents the Δ strain, which when multiplied by the modulus of elasticity yields the Δ stress. The Δ stress multiplied by the cross-sectional area of the cylinder produces the Δ load, which is used to determine weight. Let us determine the value of R_{3} under no load when the bridge is balanced and its value when the resistance of the strain gauge changes to 120.24 Ω under load.
