Wheatstone Bridge
A Wheatstone Bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. It consists of four resistors and provides a precise way to measure resistance. When the bridge is balanced, the ratio of the two known resistances is equal to the ratio of the two unknown resistances, allowing for accurate resistance measurements.
6 Key excerpts on "Wheatstone Bridge"
eBook - ePub- Lawrence Thompson(Author)
- 2006(Publication Date)
- International Society of Automation(Publisher)
...Chapter 8 DC BRIDGES Bridges are an integral part of measurement and measurement devices. Of the many DC bridges in existence, the Wheatstone Bridge is the most often used. One use is to measure unknown resistance values. This chapter explains the operation of the Wheatstone and Kelvin bridges. You must understand bridge operation thoroughly because they are fundamental to many measurements, devices, and techniques. As a plus, they will exercise your understanding of Ohm’s Law and its applications. Wheatstone Bridge A bridge is essentially a two-branch balancing network, which is in balance when there is no difference in potential between a point on one branch and the same point on the other branch. The advantage of the bridge’s operation lies in the fact that when balance is indicated, the indicator draws no current, a condition called null. A Wheatstone Bridge used to measure resistance is illustrated in Figure 8–1. Ra and Rb in the figure are called the ratio arms. Rs is a variable standard resistance. It has a calibrated scale, so as you vary the resistance the scale tells you the resistance within the accuracy of the scale. Rx is the unknown resistance. Bridges, like the Wheatstone, are used extensively in measurement because they are a comparison measurement, that is, you are comparing an unknown value to a known value, much as in comparison calibration. The accuracy of the Wheatstone Bridge depends primarily on the tolerance of Ra, Rb, and Rs. The meter [M in Figure 8–1 ] is a null meter. It has a center zero and reads to the left for a negative voltage and to the right for a positive voltage. Some electronic volt-ohm-meters (VOMs), or electronic multimeters, and almost all digital meters (as they read + or – from 0V) will have a center-zero scale and may be used as null meters. The scale itself is unimportant, since the meter’s only purpose is to determine when there is no potential between points A and B, not the magnitude of the potential voltage...
eBook - ePub- M.B. Kirkham(Author)
- 2014(Publication Date)
- Academic Press(Publisher)
...(For a biography of Ohm, see the Appendix, Section 22.8.) 22.2. Measurement of Resistance with the Wheatstone Bridge To measure R (resistance in ohms; the Greek letter capital omega, Ω, is used to symbolize resistance in ohms), we use a Wheatstone Bridge, which is an instrument for measuring the value of an unknown resistance by comparing it with a standard. This method, devised in 1833 by S. Hunter Christie, was brought to public attention by the English physicist, Sir Charles Wheatstone (1802–1875) and has remained associated with his name (Hausmann and Slack, 1948, p. 388). (For a biography of Wheatstone, see the Appendix, Section 22.9.) The Wheatstone Bridge is the most convenient, and at the same time accurate, way of measuring resistances of widely different values (Ingersoll et al., 1953). It works on the principle of a divided circuit, which is illustrated in Figure 22.3. The current from the battery divides between the two branches abc and adc. Because the potential drop is the same along the two branches, corresponding intermediate points b and d may be found that are at the same potential. Under these circumstances, no current will flow through the galvanometer, G, connected between b and d. The bridge is then said to be balanced, and R 1 / R 2 = R 3 / X. (22.3) FIGURE 22.3 Wheatstone Bridge circuit. From Ingersoll et al. (1953, p. 134). This material is reproduced with permission of The McGraw-Hill Companies. FIGURE 22.4 A Wheatstone Bridge. From a brochure of Leeds and Northrup Co., North Wales, Pennsylvania. Courtesy of Honeywell International, Inc. Thus, any one of the four resistances may be obtained in terms of the three others. A Wheatstone Bridge often looks like a black box with knobs on the top (Figure 22.4), but there are also “slide-wire” Wheatstone Bridges. In the slide-wire form of the bridge, one of the branches (e.g., abc in Figure 22.3), consists of a wire of uniform cross-section. The point b is located by a sliding contact...
- Myer Kutz, Myer Kutz(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
...Using Equation (11.14) and assuming a gage factor S g = 2.0 This shows that the change in resistance caused by 1 με is only about 2 parts per million. For example, a strain gage with an initial resistance of precisely 120Ω will exhibit a resistance of about 119.9998Ω if subjected to a tensile strain of 1 με. It is very difficult to measure these small resistance changes directly. Consequently strain gages are usually wired into special electrical circuits that convert the small resistance change into a relatively larger voltage change that is easier to accurately measure. The Wheatstone Bridge is the most widely applied circuit of this type and will be reviewed here. A basic Wheatstone Bridge circuit is shown in Figure 11.10. Four resistances (R 1 to R 4) are wired into a four-arm pattern. An excitation voltage (V) is applied across junctions a and c, and an output voltage (E) is monitored between junctions b and d. FIGURE 11.10 The Wheatstone Bridge circuit. Output voltage E is related to the excitation voltage V as follows: (11.23) The bridge is said to be “balanced,” if the output voltage is E = 0. From Equation (11.23) it is seen that this occurs if R 1 R 3 = R 2 R 4. That is, the bridge is balanced if (11.24) In strain gage applications, the bridge is initially balanced. Often (but not always) the four resistances are initially identical (R 1 = R 2 = R 3 = R 4). As discussed later, one or more of the resistances may be a strain gage. If any of the four resistances change the bridge may become unbalanced (Ε ≠ 0). Suppose that all four resistances are strain gages, that the initial resistance of all gages is identical (R 1 = R 2 = R 3 = R 4 = R, say), and that all four gages experiences a strain and consequently exhibit a change in resistance. It can be shown (Sharpe, 2008; Shukla and Dally, 2010; Dally and Riley, 2005) that the resulting output voltage is given by (11.25) The quantity η represents a nonlinear term...
- Patrick F. Dunn(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
...The resulting four equations are E i = I 1 R 1 + I 2 R 2, (3.21) E i = I 3 R 3 + I 4 R 4, (3.22) E o = I 4 R 4 − I 2 R 2, (3.23) and E o = − I 3 R 3 + I 1 R 1. (3.4) FIGURE 3.11 The Wheatstone Bridge configuration. Kirchhoff’s first law leads to I 1 = I 2 and I s = I 4, assuming no current flows through the voltmeter. These two current relations can be used in Equations 3.21 and 3.22 to give I 1 = E i R 1 + R 2 (3.25) and I 3 = E i R 1 + R 2. (3.26) These two expressions can be substituted into Equation 3.24, yielding the desired result E o = E i [ R 1 R 1 + R 2 − R 3 R 3 + R 4 ]. (3.27) Equation 3.27 leads to some interesting features of the Wheatstone Bridge. When there is no voltage output from the bridge, the bridge is considered to be balanced even if there is an input voltage present. This immediately yields the balanced bridge equation R 1 R 2 = R 3 R 4. (3.28) This condition can be exploited to use the bridge to determine an unknown resistance, say R 1, by having two other resistances fixed, say R 2 and R 3, and varying R 4 until the balanced bridge condition is achieved. This is called the null method. This method is used to determine the resistance of a sensor which usually is located remotely from the remainder of the bridge. An example is the hot-wire sensor of an anemometry system used in the constant-current mode to measure local fluid temperature. FIGURE 3.12 Cantilever beam with four strain gages. The bridge can be used also in the deflection method to provide an output voltage that is proportional to a change in resistance. Assume that resistance R 1 is the resistance of a sensor, such as a fine wire or a strain gage. The sensor is located remotely from the remainder of the bridge circuit in an environment in which the temperature increases from some initial state...
eBook - ePub- C R Robertson(Author)
- 2008(Publication Date)
- Routledge(Publisher)
...Ω, R 3 = 4 Ω and R 4 = 2 Ω. So for balance, the ratio of the two resistors on the left-hand side of the bridge equals the ratio of the two on the right-hand side. However, a better way to express the balance condition in terms of the resistor values is as follows. If the product of two diagonally opposite resistors equals the product of the other pair of diagonally opposite resistors, then the bridge is balanced, and zero current flows through the central limb and transposing equation (2.11) to make R 4 the subject we have Thus if resistors R 1, R 2 and R 3 can be set to known values, and adjusted until a sensitive current measuring device inserted in the central limb indicates zero current, then we have the basis for a sensitive resistance measuring device. Worked Example 2.13 Q A Wheatstone Bridge type circuit is shown in Fig. 2.28. Determine (a) the p.d. between terminals B and D, and (b) the value to which R 4 must be adjusted in order to reduce the current through R 3 to zero (balance the bridge). Fig. 2.28 A The circuit is sketched and currents marked, applying Kirchhoff’s current law, as shown in Fig. 2.29. Kirchhoff’s voltage law is now applied to any three loops. Note that as in this case there are three unknowns (I 1, I 2, and I 3) then we must have at least three equations in order to solve the problem. Using equations [1] and [2] to eliminate I 1 we have: Fig. 2.29 and now using equations [3] and [4] we can eliminate I 2 as follows: (b) For balance conditions 2.9 The Wheatstone Bridge Instrument This is an instrument used for the accurate measurement of resistance over a wide range of resistance values. It comprises three arms, the resistances of which can be adjusted to known values. A fourth arm contains the ‘unknown’ resistance, and a central limb contains a sensitive microammeter (a galvanometer or ‘galvo’). The general arrangement is shown in Fig. 2.30. Comparing this circuit with that of Fig...
- Dale Crane, Dennis Wilt(Authors)
- 2017(Publication Date)
- Aviation Supplies & Academics, Inc.(Publisher)
...One pair of diagonally opposite corners is connected to an input device and the other two corners are connected to the output device. Bridge circuits are a special type of complex circuit that are often used in electrical measuring and controlling devices. Figure 2-25 shows a typical bridge circuit used to measure temperature. Figure 2-25. Bridge circuits are used as measuring circuits. The current through the indicator varies as the resistance of R 4 changes. Resistor R 4 is a temperature probe, a coil of very fine wire whose resistance changes as its temperature changes. When the bridge is connected across a battery, current finds two paths through which it can flow. It can flow through resistors R 1 and R 2 or through resistors R 3 and R 4. If the value of the four resistors is such that the ratio of the resistance R 1 to R 2 is the same as the ratio of R 3 to R 4, then the voltage at point C will be the same as the voltage at point D. Because there is no voltage drop across the indicator, no current will flow through it. In this condition, the bridge is said to be balanced. Resistor R4 is variable, and as it changes from the value that balanced the bridge, a voltage drop will be developed across the indicator that causes current to flow through it. As the resistance of R 4 goes up, current flows from D to C, and as the value of R 4 goes down below the balance value, current flows from C to D. Finding the Equivalent Resistance of a Bridge Circuit A bridge circuit cannot be changed into a simple series or parallel circuit because of the resistor R X in Figure 2-26. This resistor is the same as the indicator in Figure 2-25. Figure 2-26. To find the equivalent resistance of a bridge circuit, the delta portion of the circuit, RX, RY, and RZ, must be converted into an equivalent Y-circuit, RA, RB, and RC. Y-circuit. A type of electrical circuit in which three impedances are connected with a common point and current flows through each impedance...
