Wheatstone Bridge Principle and Formula (with Diagram)
The Wheatstone bridge is an important electrical circuit used in JEE Main Physics to measure unknown resistance values with high accuracy. It operates on principles based on Kirchhoff's laws and forms a fundamental part of topics in resistance measurement, sensor circuits, and practical current electricity.
Mastery of the Wheatstone bridge formula, its derivation, and key applications can help you tackle many JEE numericals with confidence. Vedantu subject experts recommend clear understanding of balance and unbalance conditions to solve common exam problems efficiently.
Wheatstone Bridge Circuit Diagram and Configuration
A typical Wheatstone bridge contains four resistors connected in a diamond-shaped network with a voltage supply and a sensitive galvanometer. The points are commonly labeled as A, B, C, and D. The resistors are:
- P: Known resistor between A and B
- Q: Known resistor between B and C
- R: Known resistor between A and D
- S: Unknown resistor between D and C
A galvanometer is connected between junctions B and D, and a battery is applied between A and C. Understanding this set-up is vital for current electricity questions and for performing lab experiments using bridge circuits. If you struggle with diagrams, start by practicing labeling each corner with the corresponding resistor and connection.
Principle and Working of Wheatstone Bridge (Kirchhoff's Laws)
The Wheatstone bridge principle is based on the condition of no current through the galvanometer—this occurs only when the circuit is balanced. The key underlying laws are Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). When the bridge is balanced, the potential difference across the galvanometer is zero and:
- Current entering any junction equals current leaving (KCL).
- Algebraic sum of voltages in a closed loop is zero (KVL).
- Potential drop across P/Q equals R/S for balance.
- No deflection in galvanometer under balance.
- Unbalanced bridge: galvanometer shows current proportional to imbalance.
Understanding the balanced condition is vital, as many JEE problems ask you to find the unknown resistor or check for bridge balance. If current is observed in the galvanometer, the bridge is unbalanced, and KVL must be applied to analyze the circuit.
current electricity
Derivation and Formula for Wheatstone Bridge
The mathematical derivation of the Wheatstone bridge formula uses Kirchhoff's laws for the two loops ABC and ABD. Let the battery be connected between A and C, and let G be the galvanometer resistance. For the balanced condition (no current through G):
- Current through G is zero; so, same current flows in AB and AD branches.
- Apply KVL to loop ABDA: VAB = VAD
- So, I1P = I2R
- For loop BCDB: I1Q = I2S
- Under balance condition, I1P/I1Q = I2R/I2S
- Thus, P/Q = R/S
Key Wheatstone bridge equation:
| Bridge Arm | Resistance |
|---|---|
| AB | P |
| BC | Q |
| AD | R |
| DC | S (unknown) |
From the balance condition, the unknown resistance S can be found using:
S = (R × Q) / P
This formula is heavily used in both JEE problem-solving and laboratory setups like the meter bridge. Remember to substitute values with correct units (ohms) and check that the galvanometer shows zero current.
ohms law and resistance
kirchhoffs laws of electric circuits
Applications and Variants of Wheatstone Bridge
The Wheatstone bridge is widely used in instruments and engineering, including sensors and precise resistance measurement. You will encounter its usage in:
- measuring resistance of wires and unknown devices
- Strain gauges for structural load analysis
- Load cells for weighing systems
- Temperature sensors using bridge modifications
- Analog instrumentation and precise digital circuits
Practical variants include the meter bridge, potentiometer, and modified bridges for AC measurements. Always remember, balanced bridge is used for highest accuracy, while an unbalanced bridge can be used to detect small voltage changes in sensor outputs.
electrical resistance
properties of solids and liquids revision notes
Sample JEE Problem on Wheatstone Bridge
Consider a Wheatstone bridge with P = 10 Ω, Q = 20 Ω, R = 15 Ω. The bridge is balanced; find the unknown resistance S. Use the classic formula:
S = (R × Q)/P = (15 × 20)/10 = 30 Ω. This is the correct stepwise method.
When faced with complex circuits, redraw the network, mark all points, and define current directions for analysis. Pay special attention if the bridge is not balanced—draw loops and apply Kirchhoff’s law as with any tough circuit analysis question.
current electricity mock test
circuit solving
current electricity revision notes
Summary and Key Takeaways of Wheatstone Bridge
The Wheatstone bridge enables precise calculation of unknown resistance, a frequent JEE Main and advanced practical topic. Focus on identifying balance, applying the core formula S = (R × Q)/P, and confidently redrawing circuits. For revision, highlight the differences between balanced and unbalanced conditions, always check sign conventions, and relate to meter bridge or potentiometer experiments. Regular practice of JEE-style numericals and last-minute revision of derivations will help you score higher. Vedantu covers such crucial topics with IIT-faculty–verified explanations, stepwise logic, and up-to-date JEE Main patterns.
units and measurements mock test
physics syllabus
difference between series and parallel circuits
experimental skills revision notes
FAQs on Wheatstone Bridge Explained: Principle, Working, and Uses
1. What is a Wheatstone bridge used for?
The Wheatstone bridge is an electrical circuit designed to accurately measure an unknown resistance by balancing two legs of a bridge circuit. Typically used in physics experiments and engineering applications, it is essential for precise measurements. Key uses include:
- Determining unknown resistances in laboratory setups
- Measurement systems for strain gauges and load cells
- Sensor-based instrumentation (analog sensors, pressure sensors)
- Calibration of measuring devices and meters
2. What is the Wheatstone bridge formula?
The Wheatstone bridge formula relates the four resistors in the bridge circuit: The bridge is balanced when (P/Q) = (R/X) or P/Q = R/X, where:
- P and Q are known resistors
- R is a variable resistor (adjusted to balance)
- X is the unknown resistor
3. What is the principle of Wheatstone bridge from Kirchhoff's law?
The Wheatstone bridge principle is based on Kirchhoff's laws, specifically the junction rule and the loop rule. The bridge is balanced when the voltage across the bridge (galvanometer) is zero, meaning:
- The sum of voltage drops in each closed loop equals zero (Kirchhoff’s second law)
- No current flows through the galvanometer at balance
- The ratio of resistances in both arms is equal (P/Q = R/X)
4. Are Wheatstone bridges still used today?
Yes, Wheatstone bridges are still widely used in modern electronics and engineering, especially in measurement and sensor applications. Common modern uses include:
- Strain gauge circuits for measuring mechanical strain
- Load cells in weighing scales
- Analog signal conditioning for sensors
- Precise resistance and temperature measurements
5. How does the Wheatstone bridge work with strain gauges?
Wheatstone bridges are commonly used with strain gauges to measure very small changes in resistance due to mechanical deformation. The process involves:
- Integrating the strain gauge as one arm of the bridge
- Detecting resistance changes as small voltage differences
- Balancing the bridge to obtain accurate, amplified readings
6. What are the types of Wheatstone bridges?
Wheatstone bridges have several variants, each suited for specific applications:
- Simple/Standard Wheatstone Bridge (for resistance measurement)
- Strain gauge bridge (for detecting strain changes)
- Load cell bridge (for force and weight measurement)
- Meter bridge (a laboratory version for class 12 practicals)
7. How do you determine if a Wheatstone bridge is balanced or unbalanced?
A Wheatstone bridge is balanced when the ratio of the two arms is equal, resulting in zero current through the galvanometer. To check balance:
- Observe the galvanometer reading
- Adjust the variable resistor until the galvanometer reads zero
- If any current flows, the bridge is unbalanced
8. What are the practical applications of the Wheatstone bridge?
The Wheatstone bridge is crucial in many real-world scenarios, such as:
- Measuring unknown resistances in physics labs
- Strain measurements in civil and mechanical engineering
- Force measurement in load cells and industrial weighing machines
- Temperature sensing using resistance temperature detectors (RTDs)
- Signal processing in sensor systems
9. What are common mistakes in setting up a Wheatstone bridge on a breadboard?
Common mistakes when building a Wheatstone bridge on a breadboard include:
- Incorrectly placing or connecting the resistors
- Poor or loose connections causing fluctuating readings
- Incorrect orientation of the galvanometer or power supply
- Not checking connections before taking measurements
10. What is the difference between a Wheatstone bridge and a meter bridge?
The Wheatstone bridge and meter bridge are both used to measure resistance, but differ in setup and usage:
- Wheatstone bridge: General 4-resistor configuration, used in lab and circuit designs
- Meter bridge: School laboratory device using a uniform wire (usually 1 meter), applies Wheatstone bridge principle for practical resistance measurement
