Introduction
In earlier studies you will have been introduced to two resistors connected in series with a power supply to form a voltage divider such as that shown below. These are frequently used in sensing circuits where changes in the environment surrounding the sensor alter its resistance.
You should already have met the idea that the voltage at the midpoint of a voltage divider can be calculated using the equation:
The voltage at the midpoint depends upon the individual resistor values and the power supply voltage. The theory of voltage dividers can be extended to cover other circuits.
In earlier studies you will have been introduced to two resistors connected in series with a power supply to form a voltage divider such as that shown below. These are frequently used in sensing circuits where changes in the environment surrounding the sensor alter its resistance.
You should already have met the idea that the voltage at the midpoint of a voltage divider can be calculated using the equation:
The voltage at the midpoint depends upon the individual resistor values and the power supply voltage. The theory of voltage dividers can be extended to cover other circuits.
Balanced bridge formula
One important type of circuit based on
voltage
The voltage across a component is the electrical energy transferred by 1 coulomb of charge passing through the component.voltage dividers, called a Wheatstone bridge, is shown in Fig.1. It consists of four resistors arranged as two voltage dividers connected in parallel with the same
power
The power of system is a measurement of the rate at which energy is transferred from one form to another. The scientific unit
of power is the watt.power supply. The 10 kΩ and 20 kΩ resistors are described as forming one arm of the
Wheatstone bridge
A Wheatstone bridge is a circuit made of two voltage dividers connected in parallel with the same power supply. The midpoints
of the two voltage dividers are connected with a voltmeter.Wheatstone bridge, while the variable resistor and the 6 kΩ fixed resistor make up the other arm of the bridge circuit. Alter the value of the variable resistor in Fig.1 and observe the reading on the voltmeter.
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The bridge is said to be balanced when the voltages at the midpoints of each arm have the same value. When the bridge is balanced a voltmeter connected between the two midpoints will therefore show a potential difference of 0 V.
Adjust the variable resistor in Fig.2 to balance the Wheatstone bridge.
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The example in Fig.2 is simple because the resistors in each arm have the same value. However, this need not always be the case.
For the bridge to be balanced, the resistors in each arm must have the same ratios. This can be expressed mathematically as:
This equation describes the condition needed for a Wheatstone bridge to be balanced. The resistor positions are called A, B, C, and D. The resistors at these locations are labelled as shown in Fig.4
Enter values for R_{A}, R_{B}, and R_{C} into the bridge calculator of Fig.5 and note that the value of R_{D} needed to balance the bridge depends upon the values chosen for R_{A}, R_{B}, and R_{C}.
Set the variable resistor values in Fig.6 to those shown in the table below and record the value of resistor R_{D} required for balance.
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Now check the values you have determined experimentally by entering each set of values for R_{A}, R_{B}, and R_{C} from this table into the bridge calculator of Fig.2. Note the calculated value that R_{D} must have for the bridge to be balanced in each case. Compare the calculated values with the values of R_{D} determined experimentally and recorded in the table above.
Using Wheatstone bridges
Wheatstone bridge circuits such as that shown in Fig.2 were first developed to allow very precise measurement of the resistances
of samples of materials. The method for finding an unknown resistance involves having two resistors whose values are known
precisely, and using a resistance substitution box such as is shown in Fig.7 to balance a bridge circuit. In this way, three
of the resistances in the bridge are known accurately and the fourth can be calculated using:Click on specific digits on the resistance substitution box of Fig.7 to alter its resistance.
If the precise values of the resistors A and B in the circuit of Fig.7 are known, the resistance of the substitution box can be adjusted until the bridge is balanced. The value of the unknown resistance can then be found using the balanced bridge formula.
Determining temperature
In Fig.8 a
thermistor
A thermistor is an electronic component whose resistance changes when its temperature alters. The resistance of a 'negative
temperature coefficient' (n.t.c.) thermistor reduces as the temperature increases.thermistor immersed in water forms one arm of a bridge circuit. Turn on the Bunsen to warm the water briefly. Then adjust the value
of the resistance substitution box until the bridge balances.Since the fixed resistors in the bridge have the same value, balance is achieved when the resistance of the substitution box equals that of the thermistor. Therefore when balance is achieved we know the resistance of the thermistor and can use its calibration graph to determine its temperature.
Heat the water further and note the effect on the resistance of the thermistor.
As the water is heated the thermistor's resistance decreases, so different values of the variable resistor are needed to balance the bridge at different temperatures. Balancing the bridge at any specific temperature allows the thermistor's resistance to be determined at that temperature. The actual temperature can then be found from the thermistor's resistance using the thermistor's calibration graph.
The principle behind this method could be used to determine the light level in a room. The thermistor would be replaced with an
LDR
The resistance of a light dependent resistor reduces as the light intensity increases. This feature makes LDRs ideal for use
in light sensing circuits.LDR and the light level determined from an appropriate LDR calibration graph. This basic principle governs the operation of light
meters such as that shown in Fig.9.In fact, any
sensor
Sensors used in electronics produce a change in their resistance when some feature of their surrounding environment changes.
The resistance of a thermistor changes as the surrounding temperature alters.sensor whose resistance depends upon some physical property of the surrounding environment can be used with a Wheatstone bridge
in this way to measure the value of that property, if an appropriate calibration graph is available.The
strain
The strain ε produced by a particular force is defined as the ratio of the extension to the original length.strain gauge is another example of a resistive sensor. The resistance of the strain gauge depends upon the forces acting on it.
Forces acting on a beam can be monitored with a strain gauge. In
normal
The normal to a surface at a given point is a line drawn at right angles to the surface at that point.normal operation the circuit would be arranged so that the bridge was balanced and the voltmeter reading would be 0 V. Any changes
in the forces acting on the
strain
The strain ε produced by a particular force is defined as the ratio of the extension to the original length.strain gauge would be indicated by a nonzero reading on the voltmeter.Outofbalance bridges
When a Wheatstone bridge is balanced, the ratio of the resistance values in each arm is the same. If the ratios are not equal,
the bridge is described as being 'out of balance' and a p.d. is created between the midpoints of each arm.
Click the appropriate digits on the resistance substitution box in the circuit of Fig.10 to check that your answer is correct.
When a Wheatstone bridge is out of balance, the size of the p.d. ΔV between the midpoints increases as the value of the resistance substitution box deviates further from the balance condition. The difference between the setting on the resistance substitution box and the value of resistance required for balance is referred to as ΔR.
Alter the resistance substitution box in Fig.10 between 420 Ω and 520 Ω in steps of 10 Ω and plot readings of the outofbalance voltage ΔV and outofbalance resistance ΔR for each setting.
The graph in Fig.10 is a straight line for small values of ΔR. This shows that for small changes around the balance condition the outofbalance voltage ΔV is directly proportional to the outofbalance resistance ΔR. The relationship ΔV is proportional to ΔR is true for resistance changes within approximately 5 per cent of the resistance needed to balance the bridge. When the changes from the balance condition are larger, ΔV still increases as ΔR increases but there is no longer a direct proportionality.
Before the days of the microprocessor, outofbalance bridges were used extensively in electronic instrumentation where thermistors, light dependent resistors or strain gauges were used in the bridge. When the monitored property changes by a small amount, the magnitude of the change can be indicated by the outofbalance voltage.
The potential differences produced by sensing circuits using outofbalance bridges are small. These small voltages can be amplified by the type of differential amplifier circuit shown in Fig.11.
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In addition, whether the resistance of the sensor is increasing or decreasing can be determined from the sign of the outofbalance voltage.
Summary
Two voltage dividers can be made into a bridge circuit, commonly called a Wheatstone bridge. The Wheatstone bridge is balanced when there is no p.d. between the midpoints of the voltage dividers. For this to happen, the ratio of the resistors in each voltage divider must be the same.
The value of resistance needed to balance a Wheatstone bridge circuit can be determined using the equation:
Wheatstone bridges can be used in circuits to measure environmental properties such as temperature or light level.
Two voltage dividers can be made into a bridge circuit, commonly called a Wheatstone bridge. The Wheatstone bridge is balanced when there is no p.d. between the midpoints of the voltage dividers. For this to happen, the ratio of the resistors in each voltage divider must be the same.
The value of resistance needed to balance a Wheatstone bridge circuit can be determined using the equation:
Wheatstone bridges can be used in circuits to measure environmental properties such as temperature or light level.
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