Wheatstone Bridge Principle In Detail

Wheatstone bridge is a fundamental instrument used in electrical engineering. It is a diamond shaped bridge which consists of four resistors. A known voltage is applied across the top and bottom with galvanometer connected through the remaining two arms.

In this article, we will be learning about the wheatstone bridge principle along with its uses and how it is constructed.

• What is the Wheatstone bridge?
• Where is Wheatstone Bridge used?
• Wheatstone bridge circuit diagram
• Wheatstone bridge principle
• Wheatstone bridge formula 
• Wheatstone derivation
• Wheatstone bridge limitations

What is the Wheatstone Bridge?

Known as an important instrument in electrical engineering, Wheatstone bridge is used for determining the value of unknown electrical resistance. It was invented by Samuel Hunter Christie in 1983 but this bridge was popularized in 1843 by Sir Charles Wheatstone. 

Why Wheatstone bridge is called bridge?

Wheatstone bridge is termed as bridge since its circuit configuration resembles bridge-like structure. It referes to the configuration where two branches are bridged with the help of a third branch. The aim is to balance or brifge two sides so that under certain conditions, no current flows through bridging element.

Applications: Where Wheatstone bridge is used?

• This bridge determines the value of unknown electrical resistance by comparing it with measured resistance. 
• It is useful in material testing as well as it detects minute changes in resistance indicating flaws or defects in material properties. 
• Wheatstone bridge is used for measuring temperature changes based on resistance variations with temperature.
• It is useful in AC circuit analysis as well as it can not only measure resistance but also complex impedance.
• It is used for calibrating measurement devices and instruments by providing known and accurate resistance values for comparison.

Wheatstone Bridge Circuit Diagram

Let us understand the construction according to the above-shown Wheatstone bridge diagram:

• The Wheatstone bridge is a circuit containing four resistors R1, R2, R3 and R4. These are arranged as quadrilateral (also known as four arms). 
• There are two known resistors, one variable resistor and one unknown resistor.
• They have two terminals A and C through which an electromotive force source is connected. This is known as the battery arm. 
• Between B and D, a galvanometer is connected and is known as the galvanometer arm. 
• Also known as the resistance bridge, it calculates the unknown resistance (R4) by balancing two legs of the bridge circuit. 

Wheatstone Bridge Principle 

Wheatstone Bridge works on the null deflection principle. The principle is to adjust known resistances until no current flows through galvanometer to achieve balanced condition. According to this principle of null deflection or the ‘balanced bridge’ principle, ratio of resistances in one leg is equal to ratio of resistance in other leg. 

Basically, the ratio of resistances in one leg of the bridge becomes equal to the ratio in the other leg. This is the balanced condition. As soon as this balance is achieved no current will flow via the galvanometer and it will show null deflection or zero reading.

Formula for Calculating Unknown Resistance

As shown in the above diagram, the formula for calculating the unknown resistance (i.e. R4) is given by the equation: 

Formula of Wheatstone Derivation

Let’s derive the balanced condition for a Wheatstone bridge where the unknown resistance is denoted as R4. 

• R1: Known resistance 
• R2: Known resistance
• R3: Known resistance
• R4: Unknown resistance
• V: Source voltage
• G: Galvanometer

For the bridge to be balanced, the potential at point A must be equal to the potential at point B, which means no current will flow through the galvanometer.

Let us suppose that the cell has no resistance. Syppose this is a balanced bridge and hence the current Ig = 0. Now, in this case, Kirchhoff’s junction rule will be applied to junctions D and B. We known that in this case, I1 = I3 and I2 = I4.

Applying Kirchhoff’s loop rule to the closed loop ADBA. 

–I1 x R1 + 0 + I2 x R2  = 0 (here Ig = 0) [eq. 1]

From equation 1, we can say that:

Applying Kirchhoff’s loop rule to the second closed loop CBDC.

I2 x R4 + 0 – I1 x R3= 0 [eq. 3]

From equation 3, we can say that:

From equation 2 and 4, we get 

Hence:

Wheatstone Bridge Limitations

• Sensitivity: If the galvanometer isn’t sensitive enough, it might not detect small imbalances, leading to inaccuracies in measurements of very high or very low resistances.
• Parasitic Components: Real-world components have parasitic resistances, inductances, and capacitances. These can affect the balance of the bridge, especially at higher frequencies.
• Frequency Limitations: The Wheatstone bridge is typically used with DC or low-frequency AC. At higher frequencies, capacitive and inductive effects become significant, making the bridge less accurate.
• Temperature Effects: The resistance of the components in the bridge can change with temperature. If the bridge isn’t kept at a constant temperature, or if the components aren’t temperature-compensated, measurements can be off.
• Human Error: The traditional Wheatstone bridge requires manual balancing. This can introduce errors due to human judgment, especially when determining the “null” point.
• Power Limitations: The Wheatstone bridge is a passive device, meaning it doesn’t amplify signals. If the unknown resistance is too high or too low, the signal through the galvanometer might be too small to detect, even if the bridge is out of balance.
• Non-Linearity: Some components, especially those used in sensor applications, might have non-linear resistance characteristics. The Wheatstone bridge assumes linearity, which can introduce errors in such cases.