⚡ Chapter 43: Wheatstone Bridge (Class XII)

🔷 1. Introduction

In electrical measurements, it is often necessary to determine the value of an unknown resistance accurately. Although an ohmmeter can be used for this purpose, a much more accurate method is the Wheatstone Bridge.

The Wheatstone Bridge is a network of four resistors connected in the form of a bridge. It works on the principle of balancing two arms of an electrical circuit. At balance, no current flows through the galvanometer, allowing the unknown resistance to be calculated accurately.

🔷 2. What is a Wheatstone Bridge?

Ethan: Professor, what is a Wheatstone Bridge?

Professor: A Wheatstone Bridge is an electrical circuit consisting of four resistors arranged in a bridge configuration. It is used to determine an unknown resistance by comparing it with known resistances.

Academic Definition

A Wheatstone Bridge is an electrical network of four resistors used to determine an unknown resistance by balancing two arms of the bridge so that no current flows through the galvanometer.

🔷 3. Construction of a Wheatstone Bridge

Ethan: Professor, what are the main components of a Wheatstone Bridge?

Professor: A Wheatstone Bridge consists of the following components.

  • Four resistors arranged in the form of a bridge.
  • Three resistors of known values.
  • One unknown resistor whose value is to be determined.
  • A galvanometer connected across the bridge.
  • A battery connected across the opposite corners of the bridge.

🔷 4. Working Principle

Ethan: Professor, on what principle does the Wheatstone Bridge work?

Professor: It works on the principle of balance of potential difference. When the bridge is balanced, the two junctions connected to the galvanometer are at the same electric potential.

Since both junctions have equal potential, there is no potential difference across the galvanometer.

Potential Difference across Galvanometer = 0

Therefore,

Current through Galvanometer = 0

🔷 5. Balanced Condition of Wheatstone Bridge

Ethan: Professor, what is meant by a balanced Wheatstone Bridge?

Professor: A Wheatstone Bridge is said to be balanced when no current flows through the galvanometer.

Under this condition,

P/Q = R/S

where,

  • P = First known resistance
  • Q = Second known resistance
  • R = Third known resistance
  • S = Unknown resistance

🔷 6. Formula for Unknown Resistance

Ethan: Professor, how can we calculate the unknown resistance?

Professor: Rearranging the balance equation gives:

S = (Q × R)/P

Thus, if three resistances are known, the unknown resistance can be determined accurately.

🔷 7. Why Does No Current Flow Through the Galvanometer?

Ethan: Professor, why does the galvanometer show zero current at balance?

Professor: Because both terminals of the galvanometer are at the same electric potential. Without any potential difference, there is no driving force for electric current to flow through the galvanometer.

🔷 8. Derivation of the Balance Condition

Ethan: Professor, how is the balance condition derived?

Professor: Let the current through one branch be I₁ and through the other branch be I₂.

Since no current flows through the galvanometer, the potential drop across the upper arms must be equal.

I₁P = I₂R

Similarly, the potential drop across the lower arms must also be equal.

I₁Q = I₂S

Dividing the two equations,

P/Q = R/S

This is called the balance condition of the Wheatstone Bridge.

🔷 9. Numerical Example

Ethan: Professor, if P = 2 Ω, Q = 4 Ω and R = 8 Ω, what is the unknown resistance?

Professor:

S = (Q × R)/P

S = (4 × 8)/2

S = 16 Ω

🔷 10. Advantages of Wheatstone Bridge

  • Provides highly accurate measurement of resistance.
  • Simple and reliable circuit.
  • Very sensitive to small changes in resistance.
  • Can measure unknown resistances precisely.
  • Widely used in laboratory experiments.

🔷 11. Limitations of Wheatstone Bridge

  • Not suitable for measuring extremely low resistances.
  • Not suitable for measuring extremely high resistances.
  • Requires careful balancing for accurate results.
  • Measurement accuracy decreases if the galvanometer is not sufficiently sensitive.

🔷 12. Applications

  • Measurement of unknown electrical resistance.
  • Calibration of electrical instruments.
  • Laboratory resistance measurements.
  • Strain gauge measurements.
  • Temperature sensing using resistance sensors.
  • Industrial instrumentation.

📦 13. Important Results (Must Remember)

  • A Wheatstone Bridge contains four resistors.
  • It is used to determine an unknown resistance.
  • At balance, no current flows through the galvanometer.
  • Potential difference across the galvanometer is zero at balance.
  • Balance condition: P/Q = R/S.
  • Unknown resistance: S = (Q × R)/P.
  • The bridge works on the principles of potential balance and Kirchhoff's Laws.
  • It provides highly accurate resistance measurements.

🧠 14. Conceptual Questions

🔹 Q1

Ethan: What is the purpose of a Wheatstone Bridge?

Professor: It is used to measure an unknown electrical resistance accurately.

🔹 Q2

Ethan: When is the Wheatstone Bridge said to be balanced?

Professor: When no current flows through the galvanometer.

🔹 Q3

Ethan: Why does the galvanometer show zero deflection at balance?

Professor: Because the potential difference across its terminals is zero.

🔹 Q4

Ethan: What is the balance condition of the Wheatstone Bridge?

Professor: P/Q = R/S.

🔹 Q5

Ethan: Which instrument is used to detect the balance condition?

Professor: A sensitive galvanometer.

🔷 15. Summary

The Wheatstone Bridge is a highly accurate electrical circuit used for measuring unknown resistances. It consists of four resistors arranged in a bridge configuration, with a galvanometer connected between two junctions. When the bridge is balanced, no current flows through the galvanometer because the potential difference across it is zero. The balance condition, P/Q = R/S, enables the unknown resistance to be calculated precisely. Owing to its accuracy and sensitivity, the Wheatstone Bridge remains one of the most important circuits in electrical measurements and instrumentation.

✨ End of Topic: Wheatstone Bridge ✨