Wheatstone Bridge

Introduction

The measurement of resistance is crucial for any electrical circuit. Wheatstone bridge is used to measure the value of unknown resistance. It uses voltage measurement to know the importance of resistance. This bridge is used in multiple compression and tension-based devices like fluid or air pressure sensors, strain gauges, etc.

A robust electrical circuit can calculate the resistance effectively. The simple formula of the course helps calculate the resistance value without any intricate calculations. This bridge is found in differential amplifiers, high impedance amplifiers, instrumentation amplifiers, etc.

What is the Wheatstone bridge?

It is also known as a resistance bridge as it helps measure unknown resistance values. It consists of two known resistors, one variable resistor and one unknown resistor. The Wheatstone bridge circuit is highly reliable as it offers accurate measurements. It has a significant name as it was made famous by Sir Charles Wheatstone in 1843. However, this famous bridge was invented by Samuel Hunter Christie.

Imagine an electrical circuit formed by the four legs of the resistors. The bridge is balanced if the sum of resistances balances both legs. A galvanometer measures it. It is simple to understand the construction and working of this bridge.

Formula

As this bridge finds the unknown electrical resistance, let the value of resistance be R, then,

R= PS/Q

where,

P: the value of the first known resistance

Q: the value of the second known resistance

S: the standard arm of the bridge

Hence, it is easy to calculate the value of the unknown resistance using this bridge. You need the two known resistances and one variable resistor to estimate the unknown resistance value.

Construction

This bridge has four arms with two known resistances, one variable resistance or a resistor, and the unknown resistance (whose value needs to be calculated). The essential components of the electrical bridge circuit are an electromotive force (EMF) source and a galvanometer. The current flowing through the galvanometer helps calculate the total resistance offered by the four arms of this bridge circuit when an EMF passes through it. In this way, this electrical bridge circuit calculates the value of unknown resistance in minimalist construction and calculations.

Principle

The working principle of this resistance bridge is the null deflection. When the resistance ratio in both arms is equal, no current flows through the system. It is denoted by null deflection in the galvanometer. Hence, current flows through this electrical circuit under normal conditions, and the bridge is said to be in an unbalanced state. It is said to be in a balanced state only if there is no current flowing in the circuit, denoted by null deflection in the galvanometer. Thus, the work of the variable resistance or resistor is to establish the balance of the bridge by offering required resistances in the ratio of the four arm resistances.

Derivation

Let P, Q, R and S be the resistances and AB, BC, CD and AD be the four different arms of the electrical bridge circuit. Here, P and Q are the known fixed electrical resistances, and hence AB and BC are called ratio arms. A sensitive and accurate galvanometer is connected between points B and D using a switch. The electromotive force or EMF source is connected to terminals A and C through switch S1. The variable resistor S is connected between C and D. The potential at point D is easily adjustable using this variable resistor. 

Let I1 and I2 be the current flowing through ABC and ADC paths, respectively. By varying the resistance of the CD arm, the I2 value varies as the voltage across A and C remains fixed. The change in S or variable resistor is continued until the voltage drop across it is equal to I2Q. Hence, it becomes exactly equal to the voltage drop across resistor Q and becomes I1Q. 

The galvanometer, when switch S2 is closed, thus, shows null deflection as the potential difference between B and D becomes zero. This is because both the points come at the same potential. This is the condition of the bridge being balanced. 

Hence, I1= V/(P+Q) or I1Q= VQ/( P+Q)

and I2= V/(R+S) or I2S= VS/( R+S)

Combining both these equations,

V.Q/(P+Q) = V.S/(R+S)

⇒ Q/P+Q = S/R+S

⇒ (P+Q)/Q = (R+S)/S 

⇒ P/Q + 1 = R/S + 1 

⇒ P/Q = R/S

⇒ R = SP/Q

Applications

• It can measure multiple electrical quantities like inductance, capacitance, impedance and resistances by varying the amounts defined. Hence, it is a multipurpose electrical circuit bridge.
• It is the perfect solution to find the accurate values of small unknown resistances.
• It can measure multiple physical quantities like strain, temperature and light. This is possible by adding an operational amplifier to the existing bridge circuit.

Limitations

• It may not be the ideal solution to calculate small resistances. This is because the resistance of contacts and leads becomes significant and introduces errors in the calculations. Hence, this bridge is modified to Kelvin’s bridge for calculating small resistances.
• It may not be able to find the values of high resistances. This is because the measurements of the unknown resistance become so large that the galvanometer can’t show sensitivity to the deflections. Hence, modifications to this bridge are made to ensure the galvanometer remains sensitive to the highest values of resistances.
• It may not be possible to accommodate the heating effects of the current. It changes the value of resistance that can’t be calculated with this bridge. It is often observed that excessive winds can cause permanent changes in the resistance values.
  

  Conclusion

  Wheatstone bridge is used in measuring resistance, but it is also one of the most trusted electrical circuits for accurate measurements. It is found in multiple electrical and electronics circuits globally. Its functioning is quite similar to the potentiometer as it works on the concept of different measurements.

  It can help calculate impedance, inductance, capacitance and resistance. Its modifications include Kelvin’s bridge that helps measure very small resistances. Once its functioning is understood, the functioning of its changes like Carey Foster bridge, Maxwell bridge, Anderson’s bridge, etc., can easily be understood.