Wheatstone Bridge

Introduction

The Wheatstone bridge was initially illustrated by Samuel Hunter Christie and was invented by Sir Charles Wheatstone. This bridge is designed to compare the electromagnetic forces in different metals. It measures the unknown resistance connected in electrical circuits. It has a diamond-shaped arrangement with four resistors, the so-called Diamond Method.

Wheatstone Bridge

The Wheatstone bridge is a circuit with two series-parallel resistor arrangements, connected with the ground and voltage supply terminal. It produces zero voltage difference between the two parallel branches in a balanced state. Wheatstone bridge is used to measure the unknown resistance in a  bridge circuit.

Wheatstone Bridge Formula

Let us take a Wheatstone bridge of resistances R1, R2, R3, and Rx are combined to form a bridge. It contains a battery between the P and S. A galvanometer is placed between two points Q and R. This forms a balance when the galvanometer deflects to null.

Under the Balanced Condition

Let us take the balanced Wheatstone bridge as the galvanometer shows null. The potential difference between the points Q and R is 0.

The current flowing through the fixed resistor R2 and R1 is the same, be I1. The current flowing through the variable resistor(R3)  and unknown resistor(Rx) is the same, be I2.

So,

 I1 R1 = I2 R3    …..(1)

I1 R2 = I2 Rx     .…(2)

Dividing (1) and (2), we get

( I1 R1) / (I1 R2) = (I2 R3) / (I2 Rx)

R1 / R2 = R3 /Rx

R1 Rx = R2 R3

Rx = (R2 R3) / R1       …(3)

The above equation is used to find the unknown resistance in the bridge.

Rx = (R2 R3) / R1   

Construction of Wheatstone Bridge

Wheatstone bridge consists of 4 resistors in which two resistors are known, one is an unknown resistor and one variable resistor. It consists of a galvanometer and two series-parallel arrangements of resistors. Resistors are an electric component that resists the flow of current, properly called resistance.

Let us consider the Wheatstone bridge of fixed arms namely PQRS in it. It has two kinds of resistors – known and unknown resistors, as discussed before.

In this, R1 and R2 are the fixed resistors and R3 will be the variable resistors. The variable resistors restrict and control the flow of current in it. It increases or decreases the resistance value and controls the flow of current.

Let Rx be the unknown resistor.

The arms PQ and QR are called ratio arms. The arm QS is called the galvanometer arm since we can find the galvanometer(G) between the terminals Q and S. The arm PR is called the battery arm because we find the battery in between the P and R terminal.

By adjusting the value of the variable resistor, we make the galvanometer deflection 0 or null.

Problems

1.       Take a wheatstone bridge circuit of resistances R1 = 50  , R2 = 10  and R3 = 10  .

Find the unknown resistance Rx.

Solution

We can find the unknown resistance Rx can be determined by the using the below formula

R1 / R2 = R3 / Rx

Rx = (R2 R3) / R1

  Rx =  10 * 10  / 50

  Rx = 20

The unknown resistance Rx = 20

Applications of Wheatstone Bridge

1.     To find the light intensity

Using the Wheatstone bridge, we can construct the light detector circuits to find the intensity of light.

It will be used to measure the intensity of light by using the light-dependent resistor. This light-dependent resistor uses the variations in the intensity of light into the voltage and resistance change.

For making this design, we replace one of the resistors of the Wheatstone bridge with a light-dependent resistor (LDR).  Through this, we can monitor and measure the light deviations.

2.       To measure the changes in the pressure

Previously, we were using instruments like strain gauge, potentiometer, and thermistors, To measure the changes in pressure.

Now, an operational amplifier(OP-AMP) is used with the Wheatstone bridge to measure and amplify the changes in resistors.

3.       To measure the capacitance, inductance, and impedance of a circuit
4.       To measure the strain

A strain gauge is used to measure the strain applied in a material. In this Wheatstone bridge, we replace one unknown resistor with the strain gauge. Strain is the force attained when the external force is applied to the material. When a metal conductor is compressed or stretched, there would be changes in the length, diameter, and resistivity of the material. The resistance changes to the value of a particular strain. We are using the Wheatstone bridge to measure such small changes in resistance.

Limitations of Wheatstone Bridge

• Wheatstone bridge is used to measure only the small changes in resistances, not the large changes
• If any high current passes through the resistors, it produces heat, which damages the resistors
• Resistors are costly as we are using high-tolerance resistors

Conclusion

In this article, we came across the concept of the Wheatstone bridge, its construction, and the formula used. Wheatstone bridges have a common source of current (I) and galvanometer across the two terminals to find the resistances. Apart from the Wheatstone bridge, there are many types of bridges like Kelvin bridge, Schering bridge, Hay bridge, and  Wien bridge.