Wheatstone Bridge: Class 12 Physics Notes, Definition, Working Principle, Formula & Real-Life Applications

WHEATSTONE NETWORK : (4 TERMINALNETWORK)

 

 

The arrangement as shown in the above diagram of Wheatstone bridge shows four terminals in which except two all are connected to each other through resistive elements. In this circuit if $R_1{R}_3=R_2{R}_4$  then $V_C=V_D$  and current in $R_5=0$ this is called balance point or null point. When current through the galvanometer is zero (null point or balance point) $\frac{P}{Q}=\frac{R}{S}$ , then $PS=QR\Rightarrow$  Here in this case products of opposite arms are equal. Potential difference between C and D at null point is zero. The null point is not affected by resistance $R_5,E$  and $R$ . It is not affected even if the positions of Galvanometer and battery ( $E$ ) are interchanged. Hence, here the circuit can be assumed to be following,

Note: In the JEE Mains Exam, CBSE Board exam and other entrance exams like NEET contain questions based on the NCERT concepts around 3 questions are from the Current Electricity chapter which also covers Wheatstone bridge topic.

 

Importance of Wheatstone Bridge

The following points highlight the importance of Wheatstone bridge:

• Through the Wheatstone bridge, it is possible to measure several electrical quantities such as capacitance, impedance, inductance and resistance. 
• A Wheatstone bridge helps in finding the accurate values of small, unknown resistances.
• Physical quantities such as strain, light and temperature can be measured through the Wheatstone bridge.

The following types of Wheatstone bridge configurations have been mentioned below:

The Wheatstone bridge operates on a fundamental principle of electrical circuit comparison. Wheatstone bridge consists of four resistors arranged in a diamond pattern with a voltage source connected across one diagonal and a measurement device across the other. The circuit divides into two parallel voltage dividers:

• Left branch: R₁ and R₂ form one voltage divider
• Right branch: R₃ and R₄ form a second voltage divider

Balance Condition

The Wheatstone Bridge principle is the balance condition: when the ratio of resistances in the first branch equals the ratio in the second branch, the voltage difference across the measuring points becomes zero:

$\frac{R_1}{R_2} = \frac{R_3}{R_4}$

This is also the Wheatstone bridge formula. When this condition is met, the bridge is "balanced" and no current flows through the measuring device.

Measurement Mechanism

The working principle leverages this balance condition:

1. In measurement applications, one or more resistors are replaced with sensors that change resistance in response to physical parameters.
2. This change disrupts the balance.
3. The resulting voltage across the measurement diagonal is proportional to the degree of imbalance.
4. This voltage can be calibrated to the physical quantity being measured.

As per NCERT, the Wheatstone bridge definition is as mentioned below:

“The Wheatstone bridge is an arrangement of four resistances – R1 , R2 , R3 , R4 as shown in the text. The null-point condition is given by:

$\frac{R_1}{R_2} = \frac{R_3}{R_4}$

using which the value of one resistance can be determined, knowing the other three resistances.”

$\frac{R_1}{R_2} = \frac{R_3}{R_4}$

This equation represents Wheatstone bridge formula which is the balance condition for a Wheatstone bridge circuit. When the ratio of the first two resistors (R₁/R₂) equals the ratio of the second two resistors (R₃/R₄), the bridge is "balanced."

• On the left side, R₁ is divided by R₂
• On the right side, R₃ is divided by R₄
• When these two ratios are equal, no current flows between the two branches

This balanced state is important because:

1. It is the principle that allows the Wheatstone bridge to make precise measurements
2. When balanced, the voltage difference across the measuring points is zero
3. If any resistor value changes (like in a sensor application), the bridge becomes unbalanced, creating a voltage that can be measured

This simple relationship makes the Wheatstone bridge useful for detecting small changes in resistance, as the balance is very sensitive to even tiny variations in any of the four resistors.