## Thursday, October 26, 2023

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 easily done 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 the 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.

Derivation, Equations & Formulas

In the diagram shown above let us consider that R1 and R2 are the known resistors, R3 is variable resistor and R4 is the unknown say RX. Now to create a wheat stone bridge condition, no current should pass through wire CD or potential at point C and D must be the same. Let the currents in path ACB be i1 and in path ADB be i2.

V1 is the potential drop in resistance R1, V2 is the potential drop in resistance R2, V3 is the potential drop in resistance R3 and VX is the potential drop in resistance RX. Therefore according to Ohm’s law we can write equations given below:

V1 = i1 x R1…(1)

Now to have zero current through CD voltage drop at R1 must be equal to voltage drop at R3. Likewise voltage drop at R2 must be equal to RX. Therefore we can equate equation (1) with equation (3) and equation (2) with equation (4).

Example: Balanced & Unbalanced Wheatstone Bridge

Let us consider one example, using the same circuit diagram in above explanation, R1 = 50 ohms, R2 = 100 ohms, R3 = 40 ohms and R4 (or RX) = 120 ohms and the source voltage VS is 10 volts.

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 R2. And the known resistances are R1 and R3. The remaining resistance R4 is the variable resistance, which is obtained using a rheostat. The resistance R4 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 VOUT. 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.

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 R4, can be calculated very precisely.

Though, this method requires a rheostat, and that is not readily available to everyone. 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 account for other electrical properties of components as well. Variations of Wheatstone bridgecan 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 an 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 direct resistance.

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 the home, such as 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 the absence of light. Although there are a lot of mechanisms that offer light sensitivity, we will use the Wheatstone bridge to achieve this.

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 easily done 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 the 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.

Derivation, Equations & Formulas

In the diagram shown above let us consider that R1 and R2 are the known resistors, R3 is variable resistor and R4 is the unknown say RX. Now to create a wheat stone bridge condition, no current should pass through wire CD or potential at point C and D must be the same. Let the currents in path ACB be i1 and in path ADB be i2.

V1 is the potential drop in resistance R1, V2 is the potential drop in resistance R2, V3 is the potential drop in resistance R3 and VX is the potential drop in resistance RX. Therefore according to Ohm’s law we can write equations given below:

V1 = i1 x R1…(1)

Now to have zero current through CD voltage drop at R1 must be equal to voltage drop at R3. Likewise voltage drop at R2 must be equal to RX. Therefore we can equate equation (1) with equation (3) and equation (2) with equation (4).

Example: Balanced & Unbalanced Wheatstone Bridge

Let us consider one example, using the same circuit diagram in above explanation, R1 = 50 ohms, R2 = 100 ohms, R3 = 40 ohms and R4 (or RX) = 120 ohms and the source voltage VS is 10 volts.

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 R2. And the known resistances are R1 and R3. The remaining resistance R4 is the variable resistance, which is obtained using a rheostat. The resistance R4 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 VOUT. 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.

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 R4, can be calculated very precisely.

Though, this method requires a rheostat, and that is not readily available to everyone. 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 account for other electrical properties of components as well. Variations of Wheatstone bridgecan 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 an 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 direct resistance.

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 the home, such as 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 the absence of light. Although there are a lot of mechanisms that offer light sensitivity, we will use the Wheatstone bridge to achieve this.