Wheatstone Bridge Circuit Working Principle and Application

Samuel Hunter Christie invented the Wheatstone bridge in the year 1833, which became popular with the works of Sir Charles Wheatstone in 1843.

An electrical circuit that is set up to measure the unknown value of a resistor and creates a balance between the two legs of the bridge circuit is called a Wheatstone Bridge. As shown in the figure below, three resistances are known (one is variable/adjustable) and the fourth one has to be found out. We will be doing this with the help of ohm’s law.

Compared to the other measuring instruments such as voltage divider, the concept of Wheatstone bridge is widely used because of the accuracy in its measurement of resistance.

Components of Wheatstone bridge experiment

• A resistor with an unknown resistance value.
• Two resistors (with known resistance value)
• Variable Resistor (a device like Rheostat or Preset could work)
• Voltage/DC source 
• Galvanometer (or any device which indicates the voltage difference or the flow of current)
• Connecting Wires

Circuit Construction

A Wheatstone bridge is a bridge-type structure having four resistors, three of known and one of unknown value.

Here R1, R2, and R3 have known values among which R2 is adjustable and finally Rx is the value to be measured. Along with these resistances, a galvanometer (Vg) is there between B & D, and a DC supply between A & C.

Working Principle of Wheatstone bridge

Now according to the Wheatstone bridge principle if the ratio of the two resistances (R1/R2) on one edge is equal to the ratio of the two resistances (R3/Rx) on another edge then there will be no flow of current between the midpoints of the two edges of resistance. This condition of the bridge is known as the Balanced Bridge Condition.

In the Balanced Bridge condition, the current through the galvanometer is zero and also the voltage difference between the points B & D becomes zero, i.e., at both points voltage level would be the same.

Writing equations for the balanced bridge condition would look like:

R1/R2 = R3/Rx (or) R1 * Rx =R2 * R3

Thus, Rx = R3 * (R2/R1)

This detection of zero current in galvanometer is of high precision, thus depending on the level of precision of known values, the unknown resistance can be found with the highest rate of accuracy and precision.

In the Wheatstone bridge experiment, one resistor should always be variable in order to obtain a balanced condition. The Circuit performs at its best when the regulated voltage source is used, instead of the current with repelling characteristics.

Example Circuit:

Let us consider the below circuit where the bridge is in an unbalanced condition and we need to calculate the voltage difference between Q1 and Q2, i.e., Vout and hence the value of R4 needed to make the bridge balanced.

As per the voltage division law,

Vq1 = (R3/(R3+R1)) * Vs ,where Vs =100volts (voltage source)

putting values of R3 = 40 ohms, R1=50 ohms ,and Vs= 100 volts, we get

Vq1 = 44.4 volts

Similarly, Vq2 = (R4/(R4+R2)) * Vs

putting the values, R4 =50 ohms, R2 =100 ohms, and Vs =100 volts, we get

Vq2 =33.3 volts

Thus, Vout can be found as,

Vout = Vq1 – Vq2

So, Vout = 44.4 – 33.3 = 11.1 volts

Now to make the bridge balanced, we can find a suitable value for R4 as done below:

R4 = R2 * (R3/R1)

putting the values of R1, R2, and R3, we have

R4 = 100 * (40/50)

= 80 volts

Therefore, R4 = 80 volts is the value of resistor which should be used to make the bridge in a balanced condition.

Applications of Wheatstone bridge

The circuit has many applications, which could easily be found in our daily lives. A few of them are discussed below.

Application in Measuring Strain

When the resistance varies in proportion to the strain present in the device, strain gauges are usually used. In practice, the resistance range is from 30 ohms to 300 ohms. Since the change in the value of resistance may be a fraction of the full-scale value thus the Wheatstone bridge is the best suitable for higher precision.

For this application, the strain gauge replaces the unknown resistor. Here R2 and R4 would have the same value and R3 is adjustable. Therefore, without disturbing anything else, a rheostat is varied until the galvanometer shows a null deflection. This null deflection implies that the bridge is in a balanced condition and no strain is there on the gauge.

Light Detector Application

Light Detecting sensors use the Wheatstone Bridge.

Likewise, in this application also one edge consists of the two fixed resistances and the other edge has photoresistive sensors (LDR) and a potentiometer (Variable resistor).

The resistance of LDR does vary as the intensity of light varies, and with the help of potentiometer, one can, therefore, observe that at what intensity of light the balance point is achieved.

There is another advantage where one can note, before and after what amount of light the current flows in a positive as well as in a negative direction from one edge to another.

Other Applications

• Used in Light detecting devices.
• For measuring the changes in the pressure.
• For measuring the changes in the strain of the circuit.
• Used for the Sensing of mechanical and electrical quantities.
• Also, photoresistive devices use this circuit.
• Thermometers also use Wheatstone bridges for the temperature measurements which need to be accurate.
• Values like capacitance, inductance, impedance, etc. can be measured with some variations in the Wheatstone bridge circuit.

Limitations of Wheatstone Bridge

Along with all these advantages, there are a few limitations of the Wheatstone bridge as well, such as:

• Readings may be inaccurate under unbalanced conditions.
• The range of measured resistance varies from a few ohms to megaohms.
• Susceptibility for high dc current is not there.