Wheatstone Bridge: Working Principle, Derivation, Application, Formula & Solved Examples

Wheatstone Bridge, also specified as the resistance bridge, is employed to calculate the unknown resistance by balancing two legs of the bridge, of which one leg includes the component of unknown resistance. This method was invented by Samuel Hunter Christie in the year 1833, which was later popularized by Sir Charles Wheatstone in 1843. In this circuit the two known resistors, one unknown resistor and one variable resistor connected in the form of a bridge. This bridge is extremely reliable as it gives accurate measurements.

Read about the Sound Waves here.

Construction and Working Principle of Wheatstone Bridge

A Wheatstone bridge is used to measure the unknown resistance with the help of a bridge circuit.

1. It consists of four resistors of which two known resistors, one variable resistor, and one unknown resistor.
2. A galvanometer is connected as shown in figure 18, and the combination of two series-parallel arrangements of resistors.
3. The diagram below is the representation of the Wheatstone bridge, it consists of four arms PQ, QR, RS and PS which contains fixed and variable resistors

Here R1 and R2 are the fixed resistors while R3 is the variable resistor and Rx is the unknown resistor. The resistor which can restrict and can control the flow of electric current is called a Variable Resistor. This device can either increase or decrease its resistance value and thus control the flow of current. The arms PQ and QR are known as Ratio Arms. We can see that a galvanometer is connected between terminal Q and S. Q and S is called the galvanometer arm. The battery is connected to the other two terminals P and R. P and R is the Battery Arm. To make this bridge balanced, we can adjust the value of the variable resistor so that the deflection in the galvanometer becomes zero.

Also, check out Current and Electricity here.

Wheatstone Bridge Derivation

The bridge is said to be balanced when there is no current flowing through the galvanometer.

1. This means that the potential difference or voltage between points Q and S is zero. Also, we can omit this wire while solving the circuit analysis.
2. In this case, the current flowing through the fixed resistors and is the same and let it be considered as .
3. The current flowing through the variable resistor and the unknown resistor will be the same and is .

Here  —— (1)

Now the voltage drop from point Q to point R is equal to the voltage drop from point S to R.

So —— (2)

Wheatstone Bridge Formula

Now dividing Equation 1 by Equation 2 we get,

This unknown resistance is determined in terms of other known resistors in the bridge.

Q) Consider a bridge circuit where = 50 Ω, = 10 Ω, = 20 Ω. Now find the value of unknown resistance

Ans.

Check Electromagnetic Induction for details here.

Applications of Wheatstone Bridge

1. The Wheatstone bridge is used for the precise measurement of very low resistance values.
2. Wheatstone bridge along with an operational amplifier is used to measure the physical parameters like temperature, strain, light, etc.
3. The electrical quantities like capacitance, inductance, and impedance can also be measured using the Wheatstone bridge.
4. The light detector circuit is also constructed by using Bridge circuits, to measure the intensity of light.

Limitations and Errors of Wheatstone Bridge

• One of the major limitations of the Wheatstone bridge is that it can be used to measure few ohms to megaohms and not used to measure very large resistance as the galvanometer becomes insensitive in such cases.
• The galvanometer is less sensitive leading to inaccuracy.
• Self-heating changes the value of resistance, leading to errors.
• The probability of personal errors is more.

Learn all about Electrostatics here

Wheatstone Bridge – Important Points

1. Sir Charles Wheatstone proposed the bridge. As he brought attention to the device, it was called the Wheatstone bridge.
2. Wheatstone bridge consists of four resistors of which two resistors are known resistors, one variable resistor, one unknown resistor, and a galvanometer.
3. The applications of the Wheatstone bridge include Meter Bridge, strain gauge, thermistor, potentiometer, light detector, etc.
4. The Wheatstone cannot be used to measure very large resistance.

Check out other Important topics which will help you crack the examination:
Mechanical Properties of Fluids Fluid Dynamics Thermal Properties of Matter Thermal Conductivity Quantum Mechanics	Optics Interference of Light Ray Optics Electromagnetic Devices Mechanical Properties of Solids

Meter Bridge

A meter bridge also termed a slide wire bridge is an instrument that works on the principle of a Wheatstone bridge. A meter bridge is used in finding the unknown resistance of a conductor as that of a Wheatstone bridge.

Construction of Meter Bridge

A meter bridge is an apparatus utilized in finding the unknown resistance of a coil.  Below figure 12 is the diagram of a useful meter bridge instrument.

1. It consists of wire of constantan or manganin of 1-meter length and uniform area of cross-section.
2. A meter scale is also fitted on the wooden board parallel to the length of the wire.
3. Copper strip is fitted on the wooden board to provide two gaps in strips.
4. Across one gap, a resistance box R and in another gap the unknown resistance S is connected.
5. The battery is connected to terminal A and the negative terminal at C through one way key K1
6. The circuit is now exactly the same as the Wheatstone bridge.

Check the Application of Thermodynamics article here.

Procedure for Finding the Unknown Resistance Using Meter Bridge

According to the Wheatstone bridge principle, Adjust the position of the jockey on the wire (say at D) when touching, the galvanometer shows no deflection.

Note the length AD says to the wire. Find the length DC (100 – ) of the wire. We know that at a balanced bridge,

If r is the resistance per cm length of the wire,

then AD = resistance of length of the wire

DC = resistance of the length (100 – ) of the wire DC = (100 – ) r

Knowing and R, we can calculate S.

Don’t forget to check Electric Dipole.

Potentiometer

It is a device that does not draw any current from the given circuit and still measures the potential difference and thus it is equivalent to an ideal voltmeter.

Construction

1. Primary Circuit: It is set up with a strong battery so that the potential difference between A and B is large enough for the measurement of other/secondary batteries.
2. Secondary Circuit: It is connected with a galvanometer and the jockey with stretched wire so to measure the emf of the battery.

Principle of Potentiometer

The potentiometer works on the principle that when a constant current flows through a wire of uniform cross-sectional area, the potential difference between its two points is directly proportional to the length of the wire between the two points.

You can also check details about Laws of Thermodynamics.

Use of Potentiometer to Determine EMF of the cell

In this circuit, we have to find emf , Let the length of AB = L and at galvanometer shows no deflection.

At this point, we can find emf of

Use of Potentiometer to determine the comparison of EMF’s of Two Battery

In this circuit, we have to compare the Emf’s of two batteries; both E1 and E2 values are noted one by one at zero deflection of the galvanometer.

Suppose for we get length and and the total length AB = L

We have,

Hope this helped you to understand the important concept of Wheatstone Bridge.

Do practice it now on the Testbook App through the free mock tests.  To get the details on Nuclear Physics, candidates can visit the linked article.