wheatstone bridge experiment diagram

Wheatstone Bridge | Working, Examples, Applications

• April 2, 2024
• By Ravi Teja

In this tutorial, we will learn about Wheatstone Bridge. We will see the Working principle of Wheatstone Bridge, few example circuits and some important applications.

Resistance Measurement and Its Types

In the World of analog electronics, we come across various signals, some of them are measured by changes in resistance and some of them are with changes in inductance and capacitance.

If we consider the resistance, most of the industrial sensors like temperature, strain, humidity, displacement, liquid level, etc. produces the change in value of the resistance for an equivalent change in the respective quantity. Therefore, there is a need for a signal conditioning for every resistance based sensor.

For example, the simplest device we can think of is the Light Dependent Resistor or LDR . As the name suggests, an LDR is a device, whose resistance changes according to the amount of light falling on it.

Generally, the resistance measurement is divided into three types:

• Low Resistance Measurement
• Medium Resistance Measurement
• High Resistance Measurement

If the resistance measurement is possibly from a few micro ohms to milli ohms, then it is considered as a low resistance measurement. This measurement is actually used for research purpose. If the measurement is from 1 ohm to few hundreds of KΩ is generally referred as a medium resistance measurement. Measurement of normal resistors, potentiometers, thermistors, etc. comes under this category.

And very high resistance measurement is considered from few Mega Ohms to greater than 100 Mega Ohms. For finding the medium value of the resistance different methods are used, but mostly Wheatstone bridge is used.

What is Wheatstone Bridge?

Bridge Networks or Circuits are one of the most popular and popular electrical tools, often used in measurement circuits, transducer circuits, switching circuits and also in oscillators.

The Wheatstone Bridge is one of the most common and simplest bridge network / circuit, which can be used to measure resistance very precisely. But often the Wheatstone Bridge is used with Transducers to measure physical quantities like Temperature, Pressure, Strain etc.

Wheatstone Bridge is used in applications where small changes in resistance are to be measured in sensors. This is used to convert a change in resistance to a change in voltage of a transducer. The combination of this bridge with operational amplifier is used extensively in industries for various transducers and sensors.

For example, the resistance of a Thermistor changes when it is subjected to change in temperature. Likewise, a strain gauge, when subjected to pressure, force or displacement, its resistance changes. Depending on the type of application, the Wheatstone Bridge can be operated either in a Balanced condition or an Unbalanced condition.

A Wheatstone bridge consists of four resistors (R 1 , R 2 , R 3 and R 4 ) that are connected in the shape of a diamond with the DC supply source connected across the top and bottom points (C and D in the circuit) of the diamond and the output is taken across the other two ends (A and B in the circuit).

This bridge is used to find the unknown resistance very precisely by comparing it with a known value of resistances. In this bridge, a Null or Balanced condition is used to find the unknown resistance.

For this bridge to be in a Balanced Condition, the output voltage at points A and B must be equal to 0. From the above circuit:

The Bridge is in Balanced Condition if:

To simplify the analysis of the above circuit, let us redraw it as follows:

Now, for Balanced Condition, the voltage across the resistors R 1 and R 2 is equal. If V 1 is the voltage across R 1 and V 2 is the voltage across R 2 , then:

Similarly, the voltage across resistors R 3 (let us call it V 3 ) and R 4 ( let us call it V 4 ) are also equal. So,

The ratios of the voltage can be written as:

From Ohm’s law, we get:

Since I 1 = I 3 and I 2 = I 4 , we get:

From the above equation, if we know the values of three resistors, we can easily calculate the resistance of the fourth resistor.

Alternative Way to Calculate Resistors

From the redrawn circuit, if V IN is the input voltage, then the voltage at point A is:

Similarly, the voltage at point B is:

For the Bridge to be Balanced, V OUT = 0. But we know that  V OUT = V A – V B   .

So, in Balanced Bridge Condition,

Using above equations, we get:

After simple manipulation of the above equation, we get:

From the above equation, if R 1 is an unknown resistor, its value can be calculated from the known values of R 2 , R 3 and R 4 . Generally, the unknown value is called as R X and of the three known resistances, one resistor (mostly R 3 in the above circuit) is usually a variable Resistor called as R V .

Find Unknown Resistance using Balanced Wheatstone Bridge

In the above circuit, let us assume that R 1 is an unknown resistor. So, let us call it R X . The resistors R 2 and R 4 have a fixed value. Which means, the ratio R 2 / R 4 is also fixed. Now, from the above calculation, to create a balanced condition, the ratio of resistors must be equal i.e.,

Since the ratio R 2 / R 4 is fixed, we can easily adjust the other known resistor (R 3 ) to achieve the above condition. Hence, it is important that R 3 is a variable resistor, which we call R V .

But how do we detect the Balanced Condition? This is where a Galvanometer (an old school Ammeter) can be used. By placing the Galvanometer between the points A and B, we can detect the Balanced Condition.

With R X placed in the circuit, adjust the R V until the Galvanometer points to 0. At this point, note down the value of R V . By using the following formula, we can calculate the unknown resistor R X .

Unbalanced Wheatstone Bridge

If V OUT in the above circuit is not equal to 0 (V OUT ≠ 0), the Wheatstone is said to be an Unbalanced Wheatstone Bridge. Usually, the Unbalanced Wheatstone Bridge is often used for measurement of different physical quantities like Pressure, Temperature, Strain etc.

For this to work, the Transducer must be of resistive type i.e., the resistance of the transducer changes appropriately when the quantity it is measuring (temperature, strain, etc.) changes. In place of unknown resistor in the previous resistance calculation example, we can connect the transducer.

Wheatstone Bridge for Temperature Measurement

Let us now see how we can measure temperature using an unbalanced Wheatstone Bridge. The transducer which we are going to use here is called a Thermistor, which is a temperature dependent resistor. Depending on the temperature co-efficient of the thermistor, changes in temperature will either increase or decrease the resistance of the thermistor.

As a result, the output voltage of the Bridge V OUT will become a non-zero value. This means that the output voltage V OUT is proportional to the temperature. By calibrating the voltmeter, we can display the temperature in terms of the output voltage.

Wheatstone Bridge for Strain Measurement

One of the most commonly used applications of Wheatstone Bridge is in the Strain Measurement. Strain Gauge is a device whose electrical resistance varies in proportion to the mechanical factors like Pressure, Force or Strain.

Usually, the range of strain gauge resistance is from 30 Ω to 3000 Ω. For a given strain, the resistance change may be only a fraction of the full range. Therefore, to accurately measure the fractional changes of resistance, a Wheatstone Bridge configuration is used.

The circuit below shows a Wheatstone bridge where the unknown resistor is replaced with a strain gauge.

Due to the external force, the resistance of the strain gauge changes and as a result, the bridge becomes unbalanced. The output voltage can be calibrated to display the changes in strain.

One popular configuration of Strain Gauges and Wheatstone Bridge is in Weight Scales. In this, the Strain Gauges are carefully mounted as a single unit called as Load Cells, which is a transducer which converts mechanical force to electrical signal.

Usually, weight scales consist of four load cells, where two strain gauges expand or stretch (tension type) when external force is acting and two strain gauges compress (compression type) when load is placed.

If the strain gauge is either tensed or compressed, then the resistance can increase or decrease. Therefore, this causes unbalancing of the bridge. This produces a voltage indication on voltmeter corresponds to the strain change. If the strain applied on a strain gauge is more, then the voltage difference across the meter terminals is more.  If the strain is zero, then the bridge balances and the meter shows zero reading.

This is about the resistance measurement using a Wheatstone bridge for precise measurement. Due to the fractional measurement of resistance, Wheatstone bridges are mostly used in strain gauge and thermometer measurements.

Applications

• The Wheatstone Bridge is used for measuring the very low resistance values precisely.
• Wheatstone bridge along with operational amplifier is used to measure the physical parameters like temperature, strain, light, etc.
• We can also measure the quantities capacitance, inductance and impedance using the variations on the Wheatstone Bridge.

A beginner’s guide on Wheatstone Bridge. You learned What is a Wheatstone Bridge Circuit, what is the meaning of a Balanced Bridge, how to calculate an unknown resistance using Wheatstone Bridge and also how an Unbalanced Wheatstone Bridge can be used to measure different physical quantities like Temperature and Strain.

Related Posts:

• Different Types of Transducers (Characteristics &…
• Instrumentation Amplifier Basics and Applications
• Resistors in Parallel
• Introduction to Sensors and Transducers
• Full Wave Bridge Rectifier
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4 Responses

Which circuit is used to increase the output voltage of Wheatstone’s bridge?

You can cascade a differential op amp to amplify the output voltage.

Which bridge would you prefer to use for the measurement of a test resistor having a value around 50 k Ω ?

How does the inaccuracy in the value of the known resistance affect the accuracy of the result

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Wheatstone Bridge

Scientists use many skills to investigate the world around them. They make observations and gather information from their senses. Some observations are as simple as figuring out the texture and colour of an object. However, scientists may need to take measurements if they want to know more about a substance. Measurement is one of the important aspects of science. It is difficult to conduct experiments and form theories without the ability to measure. Thus, to measure unknown resistance in a circuit, Samuel Hunter Christie invented the Wheatstone bridge in 1833, which Sir Charles Wheatstone later popularised in 1843.

What is Wheatstone Bridge?

Wheatstone bridge, also known as the resistance bridge, calculates the unknown resistance by balancing two legs of the bridge circuit. One leg includes the component of unknown resistance.

The Wheatstone Bridge Circuit comprises two known resistors, one unknown resistor and one variable resistor connected in the form of a bridge. This bridge is very reliable as it gives accurate measurements.

Construction of Wheatstone Bridge

A Wheatstone bridge circuit consists of four arms, of which two arms consist of known resistances while the other two arms consist of an unknown resistance and a variable resistance. The circuit also consists of a galvanometer and an electromotive force source. The emf source is attached between points a and b while the galvanometer is connected between points c and d . The current that flows through the galvanometer depends on its potential difference.

What is the Wheatstone Bridge Principle?

Wheatstone Bridge Derivation

The current enters the galvanometer and divides into two equal magnitude currents as I 1 and I 2 . The following condition exists when the current through a galvanometer is zero,

The currents in the bridge, in a balanced condition, are expressed as follows:

Here, E is the emf of the battery.

By substituting the value of I 1 and I 2 in equation (1), we get

Equation (2) shows the balanced condition of the bridge, while (3) determines the value of the unknown resistance.

In the figure, R is the unknown resistance, S is the standard arm of the bridge and P and Q are the ratio arm of the bridge.

Wheatstone Bridge Formula

Following is the formula used for the Wheatstone bridge:

• R is the unknown resistance
• S is the standard arm of the bridge
• P and Q is the ratio of the arm of the bridge

Wheatstone Bridge Application

• The Wheatstone bridge is used for the precise measurement of low resistance.
• Wheatstone bridge and an operational amplifier are used to measure physical parameters such as temperature, light, and strain.
• Quantities such as impedance, inductance, and capacitance can be measured using variations on the Wheatstone bridge.

Wheatstone Bridge Limitations

• For low resistance measurement, the resistance of the leads and contacts becomes significant and introduces an error.
• For high resistance measurement, the measurement presented by the bridge is so large that the galvanometer is insensitive to imbalance.
• The other drawback is the resistance change due to the current’s heating effect through the resistance. Excessive current may even cause a permanent change in the value of resistance.

Frequently Asked Questions – FAQs

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Home > Circuit Analysis > Wheatstone Bridge – Circuit, Working, Derivation and Applications

Wheatstone Bridge – Circuit, Working, Derivation and Applications

What is wheatstone bridge construction, operation, example and applications.

Table of Contents

Wheatstone Bridge

Wheatstone bridge is an electrical circuit which is used to calculate unknown resistance . It was also used to calibrate measuring instruments such as voltmeters, ammeters, etc. It uses the concept of potential balancing using variable resistance.

Samuel Hunter Christie originally invented it in 1833, but Sir Charles Wheatstone later developed it to the form we know today in 1843. It was named Wheatstone bridge for his contribution to its development. Even though the measurement of resistance these days can be done easily using the multi-meter, Wheatstone bridge can still be used to measure unknown resistances fairly accurately, down to the milli-Ohms range. It is also called Resistance Bridge because it is heavily dependent on resistors for its functioning.

These days it can be used for many other purposes other than calculating resistances. These applications are very diverse varying from measuring light intensity, strain or pressure to calibrating potentiometers and thermistors.

The fundamental idea behind the Wheatstone bridge is very intuitive if there is a basic knowledge of current and voltage properties. Its circuit is also fairly simple. There are two resistances in series. There are two sets of such resistance branches, they are connected in parallel across a voltage source.

The balanced Wheatstone bridge will produce zero voltage difference between the two parallel branches. The resistances form a diamond shape providing current to have two input paths and two output paths. A typical Wheatstone bridge is shown in the figure below.

Wheatstone Bridge Circuit Diagram

Derivation, Equations & Formulas

In the diagram shown above let us consider that R 1 and R 2 are the known resistors, R 3 is variable resistor and R 4 is the unknown say R X . Now to create a wheat stone bridge condition, no current should pass through wire CD or potential at point C and D must be same. Let the currents in path ACB be i 1 and in path ADB be i 2 .

V 1 is the potential drop in resistance R 1 , V 2 is the potential drop in resistance R 2 , V 3 is the potential drop in resistance R 3 and V X is the potential drop in resistance R X . Therefore according to Ohm’s law we can write equations given below:

V 1 = i 1 x R 1      …(1)

V 2 = i 1 x R 2      …(2)

V 3 = i 2 x R 3      …(3)

V X = i 2 x R X      …(4)

Now to have zero current through CD voltage drop at R 1 must be equal to voltage drop at R 3 . Similarly voltage drop at R 2 must be equal to R X . Therefore we can equate equation (1) with equation (3) and equation (2) with equation (4).

V 1 = V 3 => i 1 x R 1 = i 2 x R 3      …..(5)

V 2 = V 4 => i 1 x R 2 = i 2 x R X      …..(6)

Dividing equation (5) by equation (6)

( i 1 x R 1 ) / ( i 1 x R 2 ) = ( i 2  x R 3 ) / ( i 2  x R X )

=> R 1 / R 2 = R 3 / R X

=> R X = (R 2 / R 1 ) x R 3 for a balanced wheat stone bridge.

Example: Balanced & Unbalanced Wheatstone Bridge

Let us consider one example, using the same circuit diagram in above explanation, R 1 = 50 ohms, R 2 = 100 ohms, R 3 = 40 ohms and R 4 (or R X ) = 120 ohms and the source voltage V S is 10 volts.

We can carucate voltages at point C and D by using formulas:

V C = (R 2 / (R 1 + R 2 )) x V S   and V D = (R 4 / (R 3 + R 4 )) x V S

V C = (100Ω / (50Ω +100Ω)) x 10V = 6.67 volts and V D = (120Ω / (40Ω + 120Ω)) x 10V = 7.5 volts

Now V OUT = V C – V D = 6.67V – 7.5V which is not equal to zero.

This is an unbalanced wheat stone bridge .

Lets find the correct value of R 4 for which it becomes a balanced wheat stone bridge.

R 1 / R 2 = R 3 / R 4

R 4 = ((R 2 / R 1 ) x R 3 ) = (100Ω / 50Ω) x 40Ω = 80 ohms “Ω”.

If R 4 = 80 ohms, our circuit will become a balanced wheat stone bridge .

Working & Operation of a Wheatstone Bridge

The working of a Wheatstone bridge requires us to know the values of resistances of at least two resistors . We also need a rheostat and a galvanometer. The unknown resistance can be calculated using the known values and the reading of resistance of the variable resistance.

Let in the diagram of a Wheatstone bridge, the unknown resistance be R 2 . And the known resistances be R 1 and R 3 . The remaining resistance R 4 is the variable resistance, which is obtained using a rheostat. The resistance R 4 has to be adjusted until the bridge is balanced.

That means that there is no current flow through the galvanometer that is connected between the points C and D. The galvanometer calculates the voltage V OUT . At this point, using current and voltage analysis, we can write that the ratio of resistances on each leg is equal. This equality is only applicable when the Wheatstone bridge is balanced.

Writing the above statement in the form of an equation, we get

From the above equation, we can calculate the value of the unknown resistance value. As the galvanometer can be used to reach the balanced point very precisely, and if the values of the known resistances are known to a high precision as well, the value of the unknown resistance, in the above case R 4 , can be calculated very precisely.

Though, this method requires a rheostat, and that is not readily available to all. In which case, we can calculate the value of the unknown resistance using the potential difference across the midpoints of the two resistor legs.

This circuit has many uses and is frequency applied in the measurement of strain in a wire. This can also be used for resistance thermometer measurements. The process without the variable resistance, is generally faster because the rheostat’s adjustment to zero can be a difficult and tedious process when it has to be done a number of times.

The calculation of resistance using the voltage drop across the midpoints of the two resistor legs can be calculated using a programmable calculator to give precise and exact values.

The Wheatstone bridge though has its original purpose of measuring unknown resistances, it has been modified to calculate other electrical properties of components as well. Variations of Wheatstone bridge can be used to measure impedance, inductance and capacitance .

There are some other form of Wheatstone bridge that are modified to measure the fraction of combustible gases in a given sample, like in explosimeter. The Kevin Bridge is another variation of the Wheatstone bridge which is modified to measure very low resistances.

There are also many physical properties which have their own circuitry, in which the change in any one of the properties can affect the resistance. These kinds of circuits are used in Wheatstone bridge to get the unknown values of physical properties from the changes in resistance indirectly.

This method was only applicable for DC current measurements, but the concept was extended by James Clerk Maxwell to Alternating current (AC) measurements in 1865. This was developed further by Alan Blumlein in 1926. This new concept which was closely related but was an invention of its own was given the name Blumlein Bridge in honor of Alan Blumlein for his contribution.

Applications of Wheatstone Bridge

• Maxwell bridge and Wein bridge are modifications of the original Wheatstone bridge which is used for calculations with reactive measurements and not just resistors
• Carey foster bridge is another type of Wheatstone bridge and can measure very small resistances.
• Kelvin Bridge is also a type of Wheatstone bridge which is modified such that four-terminal resistance can be measured instead of the conventional two port resistors.

Some real life applications of Wheatstone bridge are as follows.

Application of Wheatstone Bridge in Light Detector

The application of light sensitive circuits is in various ways helpful for an efficient power-saving behavior. The main use of the light detecting devices is to control and regulate peripheral appliances in home, like controlling the AC when people are not present, or devices that are generally ON all the time and we tend to forget to switch them OFF.

These light sensitive devices turn OFF these types of devices in absence of light. Although there are a lot of mechanisms that offer light sensitivity, we will use the Wheatstone bridge to achieve this.

The circuit which determines the light is mainly run by a special type of resistor called Light dependent resistor (LDR). Such a circuit that uses the LDR and senses light is called Light Detector Circuit.

The working of a light dependent resistor is very simple, its resistance changes in presence and absence of light. Thus, it creates a difference in current flow during and after the light is ON. When there is no light, the LDR has a resistance value which is in mega ohms range.

When there is light surrounding the LDR, its resistance drops from a few mega ohms to mere hundreds ohms. The LDR works on the principle of photoconductivity, which is the principle behind the solar power generation . When light falls on the surface of an LDR, the energy that photons carry is used to excite the charge carriers in it and it becomes more conducting. It can also be said that its resistance decreases.

The electrons which are loosely bound in the valence shell of the semiconductor device, absorb the energy from the photons and jump to conduction band.

The Wheatstone bridge is balanced if the ratios of resistances on each leg is same. So, from the diagram above, the ratio which is obtained from Wheatstone balance is given below.

R 1 ÷ R 2 = R 3 ÷ R 4

In the above circuit diagram, there is one LDR and a potentiometer that are in the first leg. There are two known resistance of 10k ohm each in the second leg. For the purpose of the circuit, we will shine some light on the LDR artificially. This causes the internal conductance to increase and in turn decrease the resistance.

As the resistance of the LDR decreases, the voltage of the point between the potentiometer and LDR. We connect an operational amplifier between the two points. It works such that if the voltage at the top point is higher than that of the lower point, then the op-amp will give a high output, and if the voltage at the top point is at lower potential than that of the bottom point, then the op-amp will give a low output.

This Op-amp’s output is connected to an LED light to indicate the working. It is wired such that the LED will glow when the op-amp gives high output and will remain switched OFF when the output is low.

Related Posts:

• Automatic Street Light Control System using LDR & Transistor BC 547
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Application of Wheatstone Bridge in Load Cells

Load Cell is a sensor which converts a load or force acting on it into electrical signal, generally used in weighing machines. This electrical signal can be a voltage change or current change depending on the types of the load cell. Load cell is made up of an elastic member to which many strain gauges are attached.

When load is applied the elastic member is deflected and creates the strain on the locations where load is applied. There are many types of load cells but the two most used are resistive load cells and capacitive load cells.

In resistive loads whenever some force or load is applied on the sensor its resistance changes and hence it changes the output voltage. It works on the principle of piezo resistivity. In capacitive loads when the load is applied, it stores the certain amount of charge according to its capacitance and applied voltage.

Circuit Diagram

While taking some measurement, the force or weight on the load cell causes elastic deformation of metal spring present in the load cell. The strain is then converted into electrical signal by strain gauge on the metal spring.

Wheat stone bridge circuit is used to convert this strain into electrical signal. Four strain gauges are configured along with four resistors R 1 , R 2 , R 3 and R 4 as shown in the circuit diagram. When there is no load or force applied the wheat stone bridge remains in balanced condition because the voltage output is close to zero due to the same resistance value in all strain gauges.

When some load or force is applied, the resultant strain from all the strain gauges changes the resistance in one or more resistors which further makes the wheat stone bridge unbalanced. The change in resistance causes the change in output voltage. The output voltage measured digitally is small and further converted into weight using some computations.

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Wheatstone Bridge Circuit Theory and Principle

Wheatstone Bridge

A Wheatstone Bridge is widely used to measure electrical resistance accurately. It includes two known resistors , one variable resistor , and one unknown resistor connected in a bridge form. By adjusting the variable resistor until the galvanometer reads zero current , the ratio of the known resistors matches the ratio of the variable resistor and the unknown resistor. This allows easy measurement of the unknown electrical resistance .

Wheatstone Bridge Theory

The resistors P and Q are known fixed resistances and are called the ratio arms. A sensitive galvanometer is connected between points B and D through switch S 2 . The Wheatstone bridge’s voltage source connects to points A and C via switch S 1 . A variable resistor S is between points C and D. Adjusting S changes the potential at point D. Currents I 1 and I 2 flow through paths ABC and ADC, respectively.

If we vary the electrical resistance value of arm CD the value of current I 2 will also be varied as the voltage across A and C is fixed. If we continue to adjust the variable resistance one situation may comes when voltage drop across the resistor S that is I 2 . S is becomes exactly equal to voltage drop across resistor Q that is I 1 .Q. Thus the potential at point B becomes equal to the potential at point D hence potential difference between these two points is zero hence current through galvanometer is nil. Then the deflection in the galvanometer is nil when the switch S 2 is closed.

Video Presentation of Wheatstone Bridge Theory

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4.11: Wheatstone Bridge

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\(\text{FIGURE IV.9}\)

The Wheatstone bridge can be used to compare the value of two resistances – or, if the unknown resistance is compared with a resistance whose value is known, it can be used to measure an unknown resistance. R 1 and R 2 can be varied. R 3 is a standard resistance whose value is known. R 4 is the unknown resistance whose value is to be determined. G is a galvanometer . This is just a sensitive ammeter, in which the zero-current position has the needle in the middle of the scale; the needle may move one way or the other, depending on which way the current is flowing. The function of the galvanometer is not so much to measure current, but merely to detect whether or not a current is flowing in one direction of another. In use, the resistances R 1 and R 2 are varied until no current flows in the galvanometer. The bridge is then said to be “balanced” and \(R_1/R_2=R_3/R_4\) and hence the unknown resistance is given by \(R_4=R_1R_3/R_2\).

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Wheatstone Bridge

Wheatstone bridge is an electrical circuit measuring unknown electrical resistances with high precision. It can be accomplished by balancing two legs of a bridge circuit, with one leg consisting of the unknown component.

Wheatstone bridge was invented by Samuel Hunter Christie in 1833 and later popularized by Sir Charles Wheatstone in 1843, hence its name.

Construction and Principle

The Wheatstone bridge circuit consists of four resistive elements (R 1 , R 2 , R 3 , and R X ) arranged in a diamond shape, forming two parallel branches, as shown in the image below. These branches are connected to a voltage source (V in ), typically a battery, and a galvanometer (V G ), which detects current in the circuit.

The fundamental principle behind the operation of a Wheatstone bridge is the concept of balance and null deflection. When the resistances in the two branches are perfectly balanced, meaning they have equal ratios or values, no current flows through the galvanometer. It is known as a balanced bridge circuit.

Variable resistance is introduced into one of the branches, known as the standard arm of the Wheatstone bridge. By adjusting the known resistances R 1 and R 2 and the variable resistance R 3 until the galvanometer reads zero current flow, it is possible to determine the value of the unknown resistance R X .

The balanced bridge circuit allows for highly accurate measurements because it eliminates any effects caused by variations in the voltage source or fluctuations in temperature. It is advantageous in applications requiring precise resistance measurements, such as laboratory experiments or industrial settings.

The formula for the Wheatstone bridge can be derived by considering the balance condition of the bridge. When the bridge is balanced, no current flows through the galvanometer, indicating that the ratio of resistances in one leg is equal to that in the other.

Mathematically, this can be expressed as:

R 1 /R 2 = R 3 /R x

Where 

R 1 and R 2 are known resistors

R 3 is a variable resistor used for balancing

R x is the unknown resistor whose resistance we want to measure

By rearranging the equation, we can solve for Rx:

R x = (R 2 /R 1 ) * R 3

This equation allows us to calculate the resistance of the unknown resistor based on the known resistances and the balance condition of the Wheatstone bridge.

The Wheatstone bridge equation can also be used to measure resistance changes. By monitoring changes in voltage across R x or changes in current flowing through it, we can determine any variations in its resistance.

Applications

The Wheatstone bridge is a versatile circuit with numerous applications, particularly engineering. Here are some typical applications:

• Engineering : The Wheatstone bridge is extensively used in engineering to measure electrical resistance and detect small changes in resistance. It is commonly employed in circuits for precise measurements, calibration, and testing of electrical components.
• Strain Gauge Measurement : Strain gauges are widely used to measure strain and deformation in various materials. By incorporating strain gauges into a Wheatstone bridge circuit, engineers can accurately measure the strain experienced by an object under load. This application is commonly used in structural engineering, the aerospace industry, and material testing.
• Pressure Sensing : The Wheatstone bridge is utilized in pressure sensors to measure changes in pressure. By integrating a pressure-sensitive element into the bridge circuit, any variation in pressure causes a change in resistance, resulting in an output voltage that can be measured and calibrated to determine the pressure accurately. This application is commonly found in automotive, industrial, and medical devices.
• Temperature Sensing : Temperature sensors based on resistance variation, such as thermistors and RTDs (Resistance Temperature Detectors), can be connected to a Wheatstone bridge to measure temperature changes accurately. The output voltage of the bridge varies with temperature, allowing for precise temperature sensing and control in applications like HVAC systems, industrial processes, and scientific research.

Wheatstone Bridge Strain Gauge

Strain gauges play a crucial role in Wheatstone bridge measurements. Strain gauges are one of the resistive elements in the Wheatstone bridge configuration.

The working principle of a strain gauge is based on the fact that when subjected to mechanical strain or deformation, the electrical resistance of specific materials changes. Strain gauges are typically made of a thin metal foil or wire bonded to a surface or embedded in a material. When the material experiences strain, the strain gauge deforms, causing a change in its resistance.

In a Wheatstone bridge configuration, strain gauges are connected in a balanced bridge circuit. The circuit has four resistive elements – two strain gauges and two precision resistors. When no strain is applied, the bridge circuit is balanced, with no output voltage.

However, their resistance changes when strain is applied to one or both strain gauges. This imbalance in resistance causes an output voltage to be generated across the bridge. The magnitude and polarity of this voltage depend on the amount and direction of the applied strain. By measuring this output voltage and knowing the characteristics of the strain gauge, such as gauge factor and sensitivity, it is possible to determine the applied strain or deformation accurately.

Strain gauges are widely used in various applications, including structural monitoring, load cells, pressure sensors, and torque measurement devices. Their high sensitivity and ability to measure small changes in resistance make them invaluable for precise measurements in engineering and scientific fields.

• Wheatstone Bridge – Electronics-tutorials.ws  
• Wheatstone Bridge Circuit – Grc.nasa.gov
• Wheatstone Bridge | Working, Examples, Applications – Electronicshub.org
• Understanding a Wheatstone Bridge Strain Gauge Circuit – Bestech.com.au

Article was last reviewed on Thursday, August 31, 2023

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Wheatstone Bridge Diagram:

A Wheatstone Bridge diagram in its simplest form consists of a network of four resistance arms forming a closed circuit, with a dc source of current applied to two opposite junctions and a current detector connected to the other two junctions, as shown in Fig. 11.1.

Wheatstone Bridge diagram are extensively used for measuring component values such as R, L and C. Since the bridge circuit merely compares the value of an unknown component with that of an accurately known component (a standard), its measurement accuracy can be very high. This is because the readout of this comparison is based on the null indication at bridge balance, and is essentially independent of the characteris­tics of the null detector. The measurement accuracy is therefore directly related to the accuracy of the bridge component and not to that of the null indicator used.

The basic dc bridge is used for accurate measurement of resistance and is called Wheatstone’s bridge.

Wheatstone Bridge Circuit (Measurement of Resistance):

Wheatstone’s bridge is the most accurate method available for measuring resistances and is popular for laboratory use. The circuit diagram of a typical Wheatstone Bridge diagram is given in Fig. 11.1. The source of emf and switch is con­nected to points A and B, while a sensitive current indicating meter, the galva­nometer , is connected to points C and D. The galvanometer is a sensitive microammeter, with a zero centre scale. When there is no current through the meter, the galvanometer pointer rests at 0, i.e. mid scale. Current in one direction causes the pointer to deflect on one side and current in the opposite direction to the other side.

When SW 1 is closed, current flows and divides into the two arms at point A, i.e. I 1  and I 2 . The bridge is balanced when there is no current through the galvanometer , or when the potential difference at points C and D is equal, i.e. the potential across the galvanometer is zero.

To obtain the bridge balance equation, we have from the Fig. 11.1.

For the galvanometer current to be zero, the following conditions should be satisfied.

Substituting in Eq. (11.1)

This is the equation for the bridge to be balanced.

In a practical Wheatstone Bridge diagram, at least one of the resistance is made adjustable, to permit balancing. When the bridge is balanced, the unknown resistance (normally connected at R 4 ) may be determined from the setting of the adjustable resistor , which is called a standard resistor because it is a precision device having very small tolerance.

Sensitivity of a Wheatstone Bridge:

When the bridge is in an unbalanced condition, current flows through the galva­nometer, causing a deflection of its pointer. The amount of deflection is a func­tion of the sensitivity of the galvanometer. Sensitivity can be thought of as deflection per unit current. A more sensitive galvanometer deflects by a greater amount for the same current. Deflection may be expressed in linear or angular units of measure, and sensitivity can be expressed in units of S = mm/μA or degree/µA or radians/μA.

Therefore it follows that the total deflection D is D = S x 1, where S is defined above and I is the current in microamperes.

Unbalanced Wheatstone’s Bridge:

To determine the amount of deflection that would result for a particular degree of unbalance, general circuit analysis can be applied, but we shall use Thevenin’s theorem .

Since we are interested in determining the current through the galvanometer, we wish to find the Thevenin’s equivalent, as seen by the galvanometer.

Thevenin’s equivalent voltage is found by disconnecting the galvanometer from the Wheatstone Bridge diagram, as shown in Fig. 11.2, and determining the open-circuit voltage between terminals a and b.

Applying the voltage divider equation, the voltage at point a can be deter­mined as follows

Therefore, the voltage between a and b is the difference between E a and E b , which represents Thevenin’s equivalent voltage.

Thevenin’s equivalent resistance can be determined by replacing the voltage source E with its internal impedance or otherwise short-circuited and calculat­ing the resistance looking into terminals a and b. Since the internal resistance is assumed to be very low, we treat it as 0 Ω. Thevenin’s equivalent resistance circuit is shown in Fig. 11.3.

The equivalent resistance of the circuit is R 1 //R 3  in series with R 2 //R 4 i.e. R 1 //R 3 + R 2 //R 4 .

Therefore, Thevenin’s equivalent circuit is given in Fig. 11.4. Thevenin’s equivalent circuit for the bridge, as seen looking back at terminals a and b in Fig. 11.2, is shown in Fig. 11.4.

If a galvanometer is connected across the terminals a and b of Fig.11.2, or its Thevenin equivalent Fig. 11.4 it will experience the same deflection at the output of the bridge. The magnitude of current is limited by both Thevenin’s equivalent resistance and any resistance connected between a and b. The resistance between a and b consists only of the galvanometer resistance R g . The deflection current in the galvanometer is therefore given by

Slightly Unbalanced Wheatstone’s Bridge:

If three of the four resistor in a bridge are equal to R and the fourth differs by 5% or less, we can develop an approximate but accurate expression for Thevenin’s equivalent voltage and resistance.

Consider the circuit in Fig. 11.7.

The voltage at point a is

The voltage at point b is

Thevenin’s equivalent voltage be­tween a and b is the difference be­tween these voltages.

If Δ r is 5% of R or less, Δ r in the denominator can be neglected without introducing appreciable error. Therefore, Thevenin’s voltage is

The equivalent resistance can be calculated by replacing the voltage source with its internal impedance (for all practical purpose short-circuit). The Thevenin’s equivalent resistance is given by

Again, if Δr is small compared to R, Δ r can be neglected. Therefore,

Using these approximations, the Thevenin’s equivalent circuit is as shown in Fig. 11.8. These approximate equations are about 98% accurate if Δr ≤ 0.05 R.

Application of Wheatstone’s Bridge:

A Wheatstone bridge may be used to measure the dc resistance of various types of wire, either for the purpose of quality control of the wire itself, or of some assembly in which it is used. For example, the resistance of motor windings, transformers, solenoids, and relay coils can be measured.

Wheatstone Bridge diagram is also used extensively by telephone companies and others to locate cable faults. The fault may be two lines shorted together, or a single line shorted to ground.

Limitations of Wheatstone’s Bridge:

For low resistance measurement, the resistance of the leads and contacts becomes significant and introduces an error. This can be eliminated by Kelvin’s Double bridge.

For high resistance measurements, the resistance presented by the bridge becomes so large that the galvanometer is insensitive to imbalance. Therefore, a power supply has to replace the battery and a dc VTVM replaces the galvanometer. In the case of high resistance measurements in mega ohms, the Wheatstone’s bridge cannot be used.

Another difficulty in Wheatstone Bridge diagram is the change in resistance of the bridge arms due to the heating effect of current through the resistance. The rise in temperature causes a change in the value of the resistance, and excessive current may cause a permanent change in value.

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Wheatstone Bridge - Construction, Working Principle, Errors, Limitations & Applications

Wheatstone bridge is the most common, accurate, and reliable method, used for the measurement of medium resistance. The principle of operation of the Wheatstone bridge is based on the null deflection. It is used to determine unknown resistance by comparing it with the known resistance.

Construction of Wheatstone Bridge :

The below shows the circuit connections of Wheatstone Bridge. It consists of four arms in which four resistances are connected (one in each arm). A source emf and null detector (galvanometer) are connected between points AC and BD respectively.

The arms with resistances R 1 and R 2 are called ratio arms. The resistance R 3 is the standard arm resistance and R 4 is the unknown resistance to be measured.

Working of Wheatstone Bridge :

The principle of working of Wheatstone Bridge is on the null deflection or null indication i.e., when the bridge is balanced the ratio of their resistances are equal and no current flows through the galvanometer.

If the bridge is unbalanced there will be a potential difference between B and D, which causes a current to flow through the galvanometer. In order to achieve a balanced condition, the known resistance and variable resistance should be varied. The basic circuit of the Wheatstone bridge is shown below.

let, P = Resistance of arm AB Q = Resistance of BC R = Resistance of AD S = Resistance of CD E = Source (battery) G = Galvanometer (detector).

The bridge is said to be balanced, when the potential difference between points A and B is equal to the voltage across points A and D (i.e., the potential difference across the galvanometer or BD is zero). Hence, no current flows through the galvanometer, thus the no deflection in it (null-deflection).

Under balancing condition, the voltage across AB will equal to the voltage across AD i.e., I 1 P = I 2 R ...(1) When the bridge is balanced, the following conditions also exist, Where E is the emf of the source. Substituting the values of I 1 and I 2 in equation 1, we get, Where, R = Unknown resistance S = Standard arm resistance P, Q = Ratio arms.

The above expression is the equation of the Wheatstone bridge under balanced condition. Hence, from the above equation, the value of unknown resistance R can be determined if the resistances in the other three arms i.e., P, Q, and S are known.

Sensitivity of the Wheatstone Bridge :

At the balance condition, the galvanometer reads zero current. But it deflects for a small unbalance in the bridge i.e., the deflection of the galvanometer depends on its sensitivity, which is given as,

Assume, θ = Deflection of the galvanometer I g = Current through the galvanometer V g = Voltage across the galvanometer.

Sensitivity of the bridge is defined as the ratio of deflection of the galvanometer to the unit fractional change in the unknown resistance i.e.,

In order to obtain the sensitivity of the bridge, assuming a small unbalance in the bridge i.e., the unbalance ΔR is at resistance R. Due to this unbalance in the bridge, an emf V o appears across BD i.e., across the galvanometer as shown below.

Using Thevenin's method to determine the voltage, the voltage across the galvanometer or terminals BD is given as, Deflection of the galvanometer is given as, Therefore, the sensitivity of the bridge is,

Errors in wheatstone bridge :, the following factors should be taken into consideration in the precision measurement of medium resistances with the wheatstone bridge. resistance of connecting leads - a 25cm length connecting lead of 22 swg wire has a resistance of about 0.012ω and this represents more than 1 part in 1000 for a 10ω resistance. thermoelectric effects - the galvanometer deflection is affected by the thermoelectric emf's which are present in the measuring circuit due to the unbalance of the bridge. the thermoelectric effect can be minimized (or) eliminated by reversing the battery connections through a quick acting switch and adjusting the galvanometer until no change in the deflection is observed. the results are obtained by taking an average of the two readings. in this way, the thermoelectric effect may be eliminated. temperature effects - an increase in temperature is accompanied by a rise in resistance of all copper and aluminum parts. the errors caused by a change of resistance due to the change of temperature produces serious errors in measurements. in case of copper which has a temperature coefficient of 0.004%c, a change in temperature of 33.8° f will cause an error of 0.4%. contact resistance - the errors in the measurement is also occurred due to contact resistances of switches. a dial may have a contact resistance of about 0.003ω and thus a four dial resistance box has a contact resistance of about 0.012ω. this value is high, especially in the measurement of low resistances. this can be overcome by using kelvin's bridge for precision resistance measurements., limitations of wheat stone bridge :, the heating effect caused by the current flowing through the resistors results in the change of resistance of the bridge arms. this can be checked if the dissipation of power in the bridge arms is calculated in advance. this ensures the restriction of current to a safe value and thus mitigates the heating effect. while using wheatstone's bridge for the measurement of low resistance, the load and contact resistances become more significant which introduces error. in order to eliminate this drawback, kelvin's double bridge is employed. in case of high resistance measurements, the galvanometer fails to indicate the imbalance in the bridge. this is because the resistance of the bridge becomes so high that the galvanometer becomes insensitive to the imbalance. this can be avoided by replacing the battery by means of a power supply and the galvanometer with a dc vtvm (vacuum tube voltmeter). however, measurement of resistances in the range of megaohms is never possible with a wheatstone bridge., applications of wheat stone bridge :, a precise measurement of low resistance can be done with wheatstone's bridge. to locate the cable fault in telephone companies. the wheatstone bridge configuration can be used with electrical sensors like strain gauge, ldr, and a thermistor to measure strain, light, and temperature. it can also be used to measure capacitance and inductance..

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Wheatstone bridge for strain gauges

In order to measure strain with a bonded resistance strain gauge, it must be connected to an electric circuit that is capable of measuring the minute changes in resistance corresponding to strain. Strain gauge transducers usually employ four strain gauge elements electrically connected to form a Wheatstone bridge circuit (Figure 2-6).

A Wheatstone bridge is a divided bridge circuit used for the measurement of static or dynamic electrical resistance. The output voltage of the Wheatstone bridge circuit is expressed in millivolts output per volt input. The Wheatstone circuit is also well suited for temperature compensation.

For more detail, see Figure 2-6. The bridge is considered balanced when R1/R2 = Rg/R3 and, therefore, VOUT equals zero. Any small change in the resistance of the sensing strain gauge will throw the bridge out of balance, making it suitable for the detection of strain. When the bridge is set up so that Rg is the only active strain gauge, a small change in Rg will result in an output voltage from the bridge. If the gauge factor is GF, the strain measurement is related to the change in Rg as follows:

The number of active strain gauges that should be connected to the bridge depends on the application. For example, it may be useful to connect gauges that are on opposite sides of a beam, one in compression and the other in tension. In this arrangement, one can effectively double the bridge output for the same strain. In installations where all of the arms are connected to strain sensors, strain gauges temperature compensation is automatic, as resistance change due to temperature variations will be the same for all arms of the Wheatstone bridge. In a four-element Wheatstone bridge, usually two gauges are wired in compression and two in tension. For example, if R1 and R3 are in tension (positive) and R2 and R4 are in compression (negative), then the output will be proportional to the sum of all the strains measured separately. For gauges located on adjacent legs, the bridge becomes unbalanced in proportion to the difference in strain. For gauges on opposite legs, the bridge balances in proportion to the sum of the strains. Whether bending strain, axial strain, shear strain, or torsional strain is being measured, the strain gauge arrangement will determine the relationship between the output and the type of strain being measured. As shown in Figure 2-6, if a positive tensile strain occurs on gauges R2 and R3, and a negative strain is experienced by gauges R1 and R4, the total output, VOUT, would be four times the resistance of a single gauge. In this configuration the stain gauge tempeature changes are compensated.

• The Chevron Bridge circuit

The Chevron bridge is illustrated in Figure 2-7. It is a multiple channel arrangement that serves to compensate for the changes in bridge-arm resistances by periodically switching them. Here, the four channel positions are used to switch the digital voltmeter (DVM) between G-bridge (one active gauge) and H-bridge (two active gauges) configurations. The DVM measurement device always shares the power supply and an internal H-bridge. This arrangement is most popular for strain measurements on rotating machines, where it can reduce the number of slip rings required.

• Four-Wire Ohm Circuit

A four-wire ohm circuit installation might consist of a voltmeter, a current source, and four lead resistors, R1, in series with a gauge resistor, Rg (Figure 2-8). The voltmeter is connected to the ohms sense terminals of the DVM, and the current source is connected to the ohms source terminals of the DVM. To measure the value of strain, a low current flow (typically one milliampere) is supplied to the circuit. While the voltmeter measures the voltage drop across Rg, the absolute resistance value is computed by the multimeter from the values of current and voltage. The measurement is usually done by first measuring the value of gauge resistance in an unstrained condition and then making a second measurement with strain applied. The difference in the measured gauge resistances divided by the unstrained resistance gives a fractional value of the strain. This value is used with the gauge factor (GF) to calculate strain. The four-wire circuit is also suitable for automatic voltage offset compensation. The voltage is first measured when there is no current flow. This measured value is then subtracted from the voltage reading when current is flowing. The resulting voltage difference is then used to compute the gauge resistance. Because of their sensitivity, four-wire strain gauges are typically used to measure low frequency dynamic strains. When measuring higher frequency strains, the bridge output needs to be amplified. The same circuit also can be used with a semiconductor strain-gauge sensor and high speed digital voltmeter. If the DVM sensitivity is 100 microvolts, the current source is 0.44 milliamperes, the strain-gauge element resistance is 350 ohms and its gauge factor is 100, the resolution of the measurement will be 6 microstrains .

• Constant Current Circuit

Resistance can be measured by exciting the bridge with either a constant voltage or a constant current source. Because R = V/I, if either V or I is held constant, the other will vary with the resistance. Both methods can be used. While there is no theoretical advantage to using a constant current source (Figure 2-9) as compared to a constant voltage, in some cases the bridge output will be more linear in a constant current system. Also, if a constant current source is used, it eliminates the need to sense the voltage at the bridge; therefore, only two wires need to be connected to the strain gauge element . The constant current circuit is most effective when dynamic strain is being measured. This is because, if a dynamic force is causing a change in the resistance of the strain gauge (Rg), one would measure the time varying component of the output (VOUT), whereas slowly changing effects such as changes in lead resistance due to temperature variations would be rejected. Using this configuration, temperature drifts become nearly negligible.

• Application & Installation

The output of a strain gauge circuit is a very low-level voltage signal requiring a sensitivity of 100 microvolts or better. The low level of the signal makes it particularly susceptible to unwanted noise from other electrical devices. Capacitive coupling caused by the lead wires' running too close to AC power cables or ground currents are potential error sources in strain measurement. Other error sources may include magnetically induced voltages when the lead wires pass through variable magnetic fields, parasitic (unwanted) contact resistances of lead wires, insulation failure, and thermocouple effects at the junction of dissimilar metals. The sum of such interferences can result in significant signal degradation.

Most electric interference and noise problems can be solved by shielding and guarding. A shield around the measurement lead wires will intercept interferences and may also reduce any errors caused by insulation degradation. Shielding also will guard the measurement from capacitive coupling. If the measurement leads are routed near electromagnetic interference sources such as transformers, twisting the leads will minimize signal degradation due to magnetic induction. By twisting the wire, the flux-induced current is inverted and the areas that the flux crosses cancel out. For industrial process applications, twisted and shielded lead wires are used almost without exception.

Guarding the instrumentation itself is just as important as shielding the wires. A guard is a sheet-metal box surrounding the analog circuitry and is connected to the shield. If ground currents flow through the strain-gauge element or its lead wires, a Wheatstone bridge circuit cannot distinguish them from the flow generated by the current source. Guarding guarantees that terminals of electrical components are at the same potential, which thereby prevents extraneous current flows. Connecting a guard lead between the test specimen and the negative terminal of the power supply provides an additional current path around the measuring circuit. By placing a guard lead path in the path of an error-producing current, all of the elements involved (i.e., floating power supply, strain gauge, all other measuring equipment) will be at the same potential as the test specimen. By using twisted and shielded lead wires and integrating DVMs with guarding, common mode noise error can virtually be eliminated.

• Lead-Wire Effects

Strain gauges are sometimes mounted at a distance from the measuring equipment. This increases the possibility of errors due to temperature variations, lead desensitization, and lead-wire resistance changes. In a two-wire installation (Figure 2-10A), the two leads are in series with the strain-gauge element, and any change in the lead-wire resistance (R1) will be indistinguishable from changes in the resistance of the strain gauge (Rg). To correct for lead-wire effects, an additional, third lead can be introduced to the top arm of the bridge, as shown in Figure 2-10B. In this configuration, wire C acts as a sense lead with no current flowing in it, and wires A and B are in opposite legs of the bridge. This is the minimum acceptable method of wiring strain gauges to a bridge to cancel at least part of the effect of extension wire errors. Theoretically, if the lead wires to the sensor have the same nominal resistance, the same temperature coefficient, and are maintained at the same temperature, full compensation is obtained. In reality, wires are manufactured to a tolerance of about 10%, and three-wire installation does not completely eliminate two-wire errors, but it does reduce them by an order of magnitude. If further improvement is desired, four-wire and offset-compensated installations (Figures 2-10C and 2-10D) should be considered. In two-wire installations, the error introduced by lead-wire resistance is a function of the resistance ratio R1/Rg. The lead error is usually not significant if the lead-wire resistance (R1) is small in comparison to the gauge resistance (Rg), but if the lead-wire resistance exceeds 0.1% of the nominal gauge resistance, this source of error becomes significant. Therefore, in industrial applications, lead-wire lengths should be minimized or eliminated by locating the transmitter directly at the sensor.

• Temperature and the Gauge Factor

Strain-sensing materials, such as copper, change their internal structure at high temperatures. Temperature can alter not only the properties of a strain gauge element, but also can alter the properties of the base material to which the strain gauge is attached. Differences in expansion coefficients between the gauge and base materials may cause dimensional changes in the sensor element. Therefore, a emperature compensation circuit would be needed. Expansion or contraction of the strain-gauge element and/or the base material introduces errors that are difficult to correct. For example, a change in the resistivity or in the temperature coefficient of resistance of the strain gauge element changes the zero reference used to calibrate the unit. The gauge factor is the strain sensitivity of the sensor. The manufacturer should always supply data on the temperature sensitivity of the gauge factor. Figure 2-11 shows the variation in gauge factors of the various strain gauge materials as a function of operating temperature. Copper-nickel alloys such as Advance have gauge factors that are relatively sensitive to operating temperature variations, making them the most popular choice for strain gauge materials.

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• Potential Energy of a System of Charges
• Potential Energy in an External Field
• Electrostatics of Conductors
• Dielectrics and Polarisation
• Capacitor and Capacitance
• What is a Parallel Plate Capacitor?
• Capacitors in Series and Parallel
• Energy stored in a Capacitor

Chapter 3 - CURRENT ELECTRICITY

• Electric Current
• Electric Current in Conductors
• Ohm's Law - Definition, Formula, Applications, Limitations
• Drift Velocity
• Limitations of Ohm's Law
• Resistivity
• Temperature Dependence of Resistance
• Electrical Energy and Power
• Electromotive Force
• Combination of Cells in Series and Parallel
• Kirchhoff's Laws

Wheatstone Bridge

Chapter 4 - moving charges and magnetism.

• Magnetic Force on a Current carrying Wire
• Motion of a Charged Particle in a Magnetic Field
• Biot-Savart Law
• Magnetic Field on the Axis of a Circular Current Loop
• Ampere's Circuital Law and Problems on It
• Force between Two Parallel Current Carrying Conductors
• Current Loop as a Magnetic Dipole
• Moving Coil Galvanometer

Chapter 5 - MAGNETISM AND MATTER

• Gauss's Law
• Magnetization and Magnetic Intensity

CHAPTER 6 - ELECTROMAGNETIC INDUCTION

• Experiments of Faraday and Henry
• Magnetic Flux
• Faraday’s Laws of Electromagnetic Induction
• Motional Electromotive Force
• Inductance - Definition, Derivation, Types, Examples
• AC Generator - Principle, Construction, Working, Applications

CHAPTER 7 - ALTERNATING CURRENT

• AC Voltage Applied to a Resistor
• Phasors | Definition, Examples & Diagram
• AC Voltage Applied to an Inductor
• AC Voltage Applied to a Capacitor
• Series LCR Circuits
• Power Factor in AC circuit
• Transformer

CHAPTER 8 - ELECTROMAGNETIC WAVES

• Displacement Current
• Electromagnetic Waves
• Electromagnetic Spectrum

CHAPTER 9 - RAY OPTICS AND OPTICAL INSTRUMENTS

• Spherical Mirrors
• Refraction of Light
• Total Internal Reflection
• Image formation by Spherical Lenses
• Dispersion of Light through a Prism

CHAPTER 10 - WAVE OPTICS

• Huygen's Wave Theory
• Young's Double Slit Experiment
• Diffraction of light
• Polarization of Light

CHAPTER 11 - DUAL NATURE OF RADIATION AND MATTER

• Photoelectric Effect
• Experimental Study of Photoelectric Effect
• Einstein's Photoelectric Equation
• Wave Nature of Matter and De Broglie’s Equation

CHAPTER 12 ATOMS

• What is Atom?
• Alpha Particle Scattering and Rutherford's Nuclear Model of Atom
• Atomic Spectra
• Bohr's Model of the Hydrogen Atom
• Spectrum of the Hydrogen Atom

CHAPTER 13 NUCLEI

• Nucleus: Structure and Function
• Structure of Nucleus
• Size of The Nucleus - Rutherford Gold Foil Experiment
• Nuclear Binding Energy - Definition, Formula, Examples
• Nuclear Force
• Radioactivity - Definition, Laws, Occurrence, Applications
• Nuclear Energy - Definition, Types, Applications

CHAPTER 14 - SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS

• Semiconductors
• What is Intrinsic Semiconductor ?
• Extrinsic Semiconductor
• PN Junction Diode
• CBSE Class 12 Previous Year Question Papers

Wheatstone bridge is a device that is used to find the resistance of a conductor, in 1842, scientist Wheatstone proposed a theory, which is called the principle of Wheatstone bridge after his name. we can prove or establish the formula for Wheatstone by using Kirchhoff laws. Wheatstone bridge is simply an electric circuit used to measure an unknown electric resistance by balancing two-point of a bridge. Let’s get started!

Wheatstone Bridge Definition

Wheatstone Bridge is an instrument designed to measure unknown resistance in electrical circuits. It calculates the unknown resistance by balancing the two legs of the bridge circuit where one leg contains both known resistors and the other leg contains one known (variable) and one unknown resistor. Since it estimates unknown resistance in an electric circuit, it is also known as a resistance bridge. Wheatstone bridge is a very reliable instrument as it measures the resistance very precisely.

Wheatstone Bridge Principle

Wheatstone Bridge works on the principle of null deflection i.e., there is no current flowing through the galvanometer, and its needle shows no deflection, hence the name null deflection. In the unbalanced state of the Wheatstone bridge i.e., when the potential across the galvanometer is different, the galvanometer shows the deflection, and as the bridge becomes balanced by changing the variable resistor, the potential difference across the galvanometer becomes zero i.e., the equilibrium state of Wheatstone bridge.

Construction of Wheatstone Bridge

Construction of Wheatstone Bridge requires four resistors P, Q, R, and S that are placed in the form of four sides AB, BC, AD, and DC of a quadrilateral ABCD. A cell E and key K 1 are placed between the A and C ends of this quadrilateral, and a sensitive galvanometer G and key K 2 is placed between the B and D ends. Clearly, the potential of point A will be equal to the potential of the positive plate of the cell and the potential of point C will be equal to the potential of the negative plate of the cell.

It is clear from the figure that the resistances P and Q are in series when the key K 2 is open. Similarly, resistances R and S are in series, but P and Q together (arm ABC) and R and S together (arm ADC) are connected in parallel to each other. Since the side BD of the galvanometer is placed like a bridge over the sides ABC and ADC of the quadrilateral, this circuit is called a bridge.

Wheatstone Bridge Derivation

Suppose, on pressing the cell key K 1 , a current I flows through the cell, which splits into two parts at the end A. One part I 1 flows through the resistance P in arm AB and the other part I 2 , through the resistance R in arm AD. The current I 1 again comes to end B and gets divided into two parts. One part of it I g flows through the galvanometer in arm BD and the remaining part (I 1 – I g ) flows through resistance Q in arm BC. At the end D, the current I 2 from arm AD and the current Ig from arm BD, so the current flowing through the resistance S in arm DC will be (I 2 + I g ).

So according to Kirchhoff’s law , in closed path ABDA, I 1 P + I g G – I 2 R = 0            . . . (1) And in closed path BCDB,  (I 1 – I g )Q – (I 2 + I g )S – I g G = 0          . . . (2) The values ​​of the resistors P, Q, R, and S are taken in such a way that no current flows through the galvanometer G when the key K 2 , is pressed. This is called the equilibrium state of the bridge , that is, in the equilibrium state of the bridge, the deflection in the galvanometer is zero (I g = 0). Putting I g = 0, in the above equations, I 1 P = I 2 R and I 1 Q = I 2 S or  I 1 P / I 1 Q = I 2 R / I 2 S or  P / Q = R / S

This is the necessary condition for the balance of the Wheatstone Bridge. With the help of the above formula, knowing the values ​​of three resistors P, Q, and R, the value of the fourth resistance S can be found.

Wheatstone Bridge Formula

The Wheatstone Bridge Formula for the calculation of the unknown resistor is as follows:

R = PS/Q where,  P and Q is the resistance of ratio arm S is the known resistance of the standard arm R is the unknown resistance

Advantages of Wheatstone’s Bridge

Various advantages of the Wheatstone’s Bridge are,

With the help of Wheatstone’s Bridge, we can build a Meter bridge. The biggest advantage of Wheatstone’s Bridge is to accurately measure the electric resistance instead of using costly instruments. We can measure minute changes in the bridge, even in m ohm. It is very easy to find out the unknown resistance as the rest of the three are easily known. We can measure strain and pressure using a Wheatstone bridge.

Disadvantages of Wheatstone’s Bridge

Various disadvantages of the Wheatstone’s Bridge are,

The result of Wheatstone’s Bridge can be easily affected by temperature and EMF cells. Wheatstone bridge may also get affected if the galvanometer is not of good quality. Wheatstone Bridge fails if it is not in a balanced condition. We can’t measure large resistance with the help of Wheatstone’s Bridge.  The cost of maintaining the Wheatstone Bridge is very high.

Wheatstone Bridge Applications

Wheatstone Bridge and the modification of Wheatstone Bridge are very useful tools in the field of physics and are used in a variety of measurement use cases, some of which are as follows:

The most common use of Wheatstone Bridge is to measure resistance,  as it can measure resistance very precisely. A Meter Bridge is one of the applications of Wheatstone Bridge, which can measure unknown resistance with the help of everyday materials and a galvanometer. With some modifications in Wheatstone Bridge, we can even measure quantities like Capacitance , Inductance , and Impedance. Using Wheatstone Bridge and operational amplifiers, we can measure a variety of physical parameters such as temperature strain, light, etc.

Wheatstone Bridge Limitations

Wheatstone Bridge is one of the best tools but it also has major limitations, which are as follows:

• Wheatstone Bridge is not ideal for very low resistance measurement as the resistance of contact and leads also has some amount of resistance, which can introduce a significant amount of errors in the measurement. Kelvin’s Double Bridge (a modification of Wheatstone Bridge) is used for the measurement of small resistance.
• For High resistance measurements (mega ohms and giga ohms of resistance), the resistance provided by the bridge becomes so high that the galvanometer becomes sensitive to imbalance. So, we can’t use Wheatstone Bridge in case of high resistance measurement.
• The resistance of a conductor depends on the temperature and the heating effect of the current causes the conductor to heat and heat changes the resistance of the conductor. This can introduce errors in the calculation and for excessive amounts of current the error can be very significant. Thus, it is also a flaw in the design of Wheatstone Bridge.

Also, Check

Electric Circuit Electric Resistance Temperature Dependence of Resistance

Sample Questions on Wheatstone Bridge

Question 1: Find the equivalent resistance between points A and C in the circuit shown in the figure below:

The equivalent circuit of the circuit shown in the above figure is given as:   Since, 2/3 = 4/6 This is the circuit of a balanced Wheatstone bridge.   In the balanced state, V B = V D  (where V represents potential)  So no current will flow through the 5 Ω resistance.   Now the equivalent resistance of sides AB and BC is R’ = 2 + 3 = 5 Ω.   The equivalent resistance of AD and DC arm R” = 4 + 6 = 10 Ω  If the equivalent resistance between the points A and C is R, and R is parallel combination of resistance R’ and R”, ⇒  1 / R = (1 / R’) + (1 / R”) ⇒  1/R = (1/5) + (1/10) ⇒  1/R = (2 + 1) / 10 ⇒  R = 10/3  ⇒  R = 3.33 Ω

Question 2: The electric circuit of a balanced Wheatstone bridge is shown in Figure. Calculate the resistance x.

Let the total resistance in arm BC be R. Since the bridge is balanced, therefore:   15/R = 5/10  ⇒ R = (15 × 10)/5 = 30 Ω  Now, as R is parallel combination of 60 Ω and X. ⇒  1/R = (1/X) + (1/60) ⇒  1/30 = 1/X + (1/60) ⇒  1/X = 1/30 – 1/60 ⇒  1/X = (2 – 1)/60 = 1 / 60 ⇒  X = 60 Ω 

Question 3: What is a Meter Bridge and what kind of precautions do we need to perform measurements using a Meter Bridge?

A Meter bridge is a device based on the principle of the Wheatstone bridge, with the help of which the resistance and specific resistance of a conductor can be determined. In this, a 1-meter long wire acts as the proportional side. Precautions while using Meter Bridge are:  The ends of all the connection wires should be cleaned with sandpaper.   The current should not flow in the circuit for a long time otherwise, its resistance increases due to the heating of the bridge wire. Therefore, the key in the cell circuit should be plugged in only when observations are to be made.  The jockey should not be run by rubbing it on the meter bridge wire otherwise, the thickness of the wire will not remain the same at all places.   A shunt with a galvanometer should be used initially while adjusting, but the shunt should be removed near the position of zero deflection.   Only such a resistance plug should be removed from the resistance box so that the position of zero deflection is approximately in the middle of the bridge wire. In this case, the sensitivity of the bridge is maximum and the percentage error is minimum.   All other plugs in the resistance box, except those that have been removed, should be tightly packed. 

Question 4: In the following figure, find the current through the 4Ω resistor.

Since, Q / P = S / R   ⇒ 4 / 20 =10 / 50  It is an example of balanced wheat-stone bridge. So, No current will flow through 16 Ω resistance. As we know that current divide in inverse ratio, current through 4Ω resistance is, = 1.4 × (20+4)+(50+10) / (50+10)  = 1.4 × (7/5)  = 1 A

FAQs on Wheatstone Bridge

Q1: what is wheatstone bridge.

A circuit is designed for the measurement of an unknown resistance by connecting three known and one unknown resistance in the form of a quadrilateral, and a voltage is applied to the opposite corners of the quadrilateral. This is known as the Wheatstone Bridge.

Q2: What is the principle of Wheatstone Bridge?

The Wheatstone Bridge works on the principle of null deflection, where the ratio of the resistance is equal and no current flows through the galvanometer.

Q3: What is the balanced condition of the Wheatstone Bridge?

When no current flows through the galvanometer and it shows no deflection, the Wheatstone Bridge is said to be in a balanced condition. This condition is also called the equilibrium condition as well.

Q4: When is Wheatstone Bridge most sensitive?

When all four resistances in the wheatstone bridge are almost equal, then the wheatstone bridge is said to be most sensitive.

Q5: Which instrument is used as a null detector in Wheatstone Bridge?

The galvanometer is used as a null detector in the Wheatstone Bridge, where a null point is the condition where no current passes through the circuit where the galvanometer is connected.

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