# Wheatstone Bridge: WORKING PRINCIPLE AND APPLICATION

The Wheatstone bridge was formerly invented by Samuel Hunter Christie in the year 1833 and later improvised by
Sir Charles Wheatstone in 1843 after which it became popular.

A Wheatstone bridge is an electrical circuit used to measure an unknown resistance value by maintaining a balance between two legs of a bridge circuit. The primary advantage of using the Wheatstone bridge is its accuracy in finding the unknown (electrical resistance) value when compared to instruments like a simple voltage divider.

## Construction of Wheatstone Bridge Wheatstone bridge is designed in a bridge type structure having four resistances, three known and one unknown.

Here R1, R2 are known resistances, R3 is variable (adjustable) and R2 is the one which needs to be measured. Apart from the resistance, there is a voltmeter connected between the points C & B and the DC supply is connected between A & D.

## Working Principle of Wheatstone Bridge

As explained above, in a Wheatstone Bridge R1, R2 and R3 are the resistances of known value and the resistance R2 is the one which has to be adjusted until no current flows through the galvanometer V.

This condition where the current through Galvanometer is zero and thus voltage between two midpoints B & C also comes to be zero is called balanced bride condition of Wheatstone bridge.

Therefore the ratio of two resistances in one leg (R1/ R2) is equal to the ratio of another two resistances in the other leg (Rx/ R3). If somehow bridge is unbalanced, the direction of the current indicates whether R2 is too high or too low.

At bridge balanced condition,

R 2 /R 1 =R x /R 3

and hence Rx= R 3 *(R 2 /R 1 ) could be measured easily.

This detection of zero current in galvanometer can be done with high precision, thus if R1, R2, and R3 are known with high precision then Rx measured will be of high precision as well. Also, even a small change in the value of Rx would disrupt the balance and could easily be detected. Alternatively, if R2 is not variable then voltage difference across or current flowing through the meter can be used to calculate Rx. This method is faster for measuring the unknown resistance of the Wheatstone bridge.

## Example of Wheatstone Bridge Consider the circuit is shown above, where the Wheatstone bridge is an unbalanced condition and output the voltage across C &amp; D and the value of R 4 are to be measured for a balanced bridge condition.

Now as per the voltage division law,

Vc = (R2 /( R1 + R2 ))*Vs

Putting R2= 12 ohms, R2 = 8 ohms, Vs= 10 volts

Vc = (12/(8+12))*10
= 6 volts

In second arm, applying voltage division law,

Vd = (R4 /( R3 + R4 ))*Vs

V2 = (16/(48+16))*10
= 2.5 volts

The voltage between points C &amp; D can be calculated as

Vcd = Vc – Vd

Vout = 6 – 2.5 = 3.5 volts.

Now to calculate R 4, for balanced bridge condition can be measured as R4 = (R3 /R1 )*R2 = 72 ohms.

So here we can conclude that the Wheatstone bridge acts like a 2 port network having 2 inputs (A & B) and 2 outputs (C &amp; D). Also if the voltage across the output terminal is 0 volts then the bridge is called to be in a balanced condition, while in an unbalanced condition voltage may have any value (either positive, negative) depending on the circuit parameters.

## Applications of Wheatstone Bridge

### Strain Measurement

Generally, for strain measurement, strain gauges are used whose resistance varies with proportionate to strain present in the device. Practically, strain gauge resistance ranges from 30 ohms to 300 ohms. Since the change in resistance may be only a fraction of full scale thus a highly precise and accurate measuring instrument is required
and Wheatstone bridge perfectly suites for it.

In this application, the unknown resistance is replaced with a strain gauge. Here R1 and R3 have the same value and R2 is a variable one. Now without applying force to the strain gauge, a rheostat is varied until voltmeter indicates null deflection. This indicated the bridge is balanced and thus no strain on the gauge.

### Light Detector Circuit It is one of the simplest applications of the Wheatstone bridge using the photoresistive device. A light dependent resistor is placed in the place of the unknown resistor in the Wheatstone bridge. An LDR which is a passive resistive sensor is used for converting visible light levels into a change in resistance and afterward a voltage. LDR has around 900 ohms resistance in dark light (at a light intensity of 100 lux) and as less as 30 ohms in bright light.

Therefore, the connection of light dependent resistor in Wheatstone bridge would help in measuring and monitoring the changes in the light levels.

The Wheatstone bridge goes with the concept of a difference measurement, which could be highly accurate.

Some variations on the Wheatstone bridge could be used to measure capacitance, inductance, impedance, etc. Some other applications can be as follows:

• Light detector using Wheatstone Bridge
• Light measurement using a photoresistive device (a light dependent resistor is placed as a substitute for one of the resistors)
• Measuring strain with the help of Bridge (strain gauge is used in place of the variable resistor)
• It is also used for sensing mechanical and electrical quantities.
• The circuit is used to measure the changes in pressure.
• It is used in thermometers for temperature measurements with high accuracy.

## Limitations of Wheatstone bridge

• Susceptibility to high DC current is not there.
• Under the unbalanced condition, readings might be inaccurate.
• Resistance measured by Wheatstone bridge ranges from “few” ohms to “mega” ohms
• With the help of applied voltage (emf), the upper range of the bridge can be increased while the lower range can be limited by connecting a lead at the binding post.

Now, if we summarize whatever we have studied till now then we can say that the Wheatstone bridge is the most common and simplest bridge network for finding out the resistance. With its ability to measure precise changes, these are mostly used for sensor applications, where a resistance change is converted to voltage change (for a transducer).

The combination of operational amplifier along with the Wheatstone bridge is used extensively in industries for various sensors and transducers. Also as said earlier, any changes in quantities like temperature, light intensity, strain, electrical and mechanical sensing, pressure, etc. could be measured in a most accurate and precise manner.

The only change required to calculate these values is to replace the unknown resistance in the bridge circuit with the required quantity (mentioned above). This is the reason why being the simplest circuit also, Wheatstone bridge is one of the most used bridge circuits.

Ajay Dheeraj
Technical Content Developer