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Applications of the Wheatstone Bridge

### Introduction

The basic Wheatstone Bridge may have any sort of voltage as its input. On this page we will examine a number of applications for which the input is a fixed dc voltage, as shown to the right. We will examine ac applications of the Wheatstone Bridge as part of our study of AC theory.

One thing to note about any variation of the Wheatstone Bridge is that the input voltage may or may not be referenced to ground, but both outputs are necessarily floating — neither output is grounded. In addition, we aren't particularly interested in the actual voltage at either output, but at the difference between the two. When the bridge is precisely balanced, that voltage difference will be zero, and even a very sensitive current meter (generally a galvanometer) will show no current flowing in either direction.

The bridge circuit can be used in either of two ways. The first is to adjust component values until the bridge is balanced. This is typically used to determine the value of an unknown resistor in the bridge, when the other three resistances are known. The second method is to measure changes in the output voltages when one of the resistances is subjected to externally-applied forces of some kind. This approach commonly replaces one resistor with a resistive device that reacts to changes in temperature, pressure, or shape. It is used to monitor and measure such changes.

### Measuring Resistance

The schematic diagram to the left shows a Wheatstone Bridge circuit set up to measure unknown resistances in the range 10K to 100K. To use this circuit, simply connect the unknown resistance to the teminals that replace R4 in the bridge and turn on the switch. Then adjust the variable resistor until galvanometer G registers no current flowing in either direction. The unknown resistance is then read directly from a calibrated scale connected to the variable resistor. (By making the variable resistor have an absolutely linear resistance taper, we make the scale linear as well, and therefore easy to read over its entire range.)

The actual range of this circuit is slightly greater. The 9.1K fixed resistor that makes up part of R2 sets the lower end of the comparison range, and the total of 109.1K sets the high end. This is slightly greater than a 10:1 ratio, so we can always be sure that the circuit will handle at least that 10:1 range. We can change where that range starts by changing the value of R3. Thus, to measure a resistor in the range 1K to 10K, we simply replace R3 with a 1K resistor. Whatever value we select for R3, that value becomes the lower end of a 10:1 range for comparing the unknown resistance.

A practical version of this circuit would actually have a set of precision resistors for R3, to be switched in or out of circuit to set the measurement range. Also, the galvanometer is very sensitive to physical shock, and can be easily damaged. To avoid this possibility, the galvanometer may be replaced with an instrumentation amplifier or similar circuit, followed by a digital readout to indicate a balanced condition on the bridge.

Note that the voltage source of 3 volts is entirely arbitrary; it could be any voltage over a wide range. The bridge will work the same way regardless of the source voltage. The selection of 3 volts simply corresponds to a pair of 1.5-volt cells, such as might be used in an ordinary flashlight.

### Electronic Sensing

The unknown resistance doesn't have to be a plain resistor. As shown to the right, the unknown can be any resistive device — in this case, a thermistor. The thermistor is a semiconductor device whose resistance changes with changes in temperature. At the same time, the ordinary resistors that form the rest of the bridge have very little sensitivity to ordinary temperature changes, such as would be encountered with changes in the weather. As a result, this circuit can be used as an electronic thermometer.

Of course, most of the time you can use a much simpler thermometer to check the temperature. However, suppose you wanted to monitor the temperature inside a sealed box or at a remote location, and yet wanted the readout to be available in a different location? This circuit will perform the desired function easily. All that is required is to connect the thermistor to a long pair of wires so it can be placed where it is needed, and the rest of the circuit can be somewhere else.

We could make R2 variable, balance the bridge, determine the resistance of the thermistor, and then check that value of resistance against a table showing the resistance of the thermistor over the required temperature range. However, this gets tedious and cumbersome. We would much rather be able to read the temperature directly on some sort of display. We can do this by simply using a specialized scale with the galvanometer — a scale calibrated to indicate the temperature that will cause the pointer to move to a particular position, rather than the current through the meter. We can also replace the galvanometer with an amplifier such as an instrumentation amplifier, and have its readout appear directly as temperature.

The sensing device doesn't have to be a thermistor; it can be any device whose self-resistance changes in accordance with some external physical condition. This includes photosensitive devices to measure light levels, strain gauges, methods to measure the salinity (salt content) of water, liquid level sensors, and any other transducer whose response to some sort of change is a change in internal resistance.

### AC Power for the Wheatstone Bridge

The power source for the Wheatstone Bridge does not have to be dc; we could use an ac power source or even some sort of signal. The use of an ac source of some kind dramatically expands the ways in which the Wheatstone Bridge can be used. We will explore some of those applications as a part of combinations of components with alternating current.

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