⚡ Chapter 45: Meter Bridge (Class XII)
🔷 1. Introduction
Measuring an unknown electrical resistance accurately is an important task in electrical laboratories. One of the simplest and most accurate instruments used for this purpose is the Meter Bridge.
A Meter Bridge is a practical application of the Wheatstone Bridge. It uses a uniform wire of one-meter length to compare an unknown resistance with a known resistance. The bridge is balanced by moving a sliding contact (jockey) along the wire until no current flows through the galvanometer.
🔷 2. What is a Meter Bridge?
Ethan: Professor, what is a Meter Bridge?
Professor: A Meter Bridge is an electrical instrument based on the Wheatstone Bridge principle. It is used to measure an unknown resistance by balancing the bridge using a one-meter long uniform resistance wire.
Academic Definition
A Meter Bridge is a practical form of the Wheatstone Bridge that uses a one-meter long uniform wire to determine an unknown resistance by comparing it with a known resistance.
🔷 3. Construction of a Meter Bridge
Ethan: Professor, what are the main parts of a Meter Bridge?
Professor: A Meter Bridge consists of the following components.
- A uniform wire exactly 1 meter long.
- A wooden or insulated base.
- Two metallic strips forming two gaps.
- A known resistance (R).
- An unknown resistance (X).
- A galvanometer.
- A jockey (sliding contact).
- A battery (cell).
- A plug key.
🔷 4. Principle of Meter Bridge
Ethan: Professor, on what principle does the Meter Bridge work?
Professor: It works on the principle of the Wheatstone Bridge. When the bridge is balanced, no current flows through the galvanometer.
Since the wire is uniform, its resistance is directly proportional to its length.
Resistance ∝ Length
🔷 5. Balance Condition
Ethan: Professor, what happens when the bridge is balanced?
Professor: At the balance point, the galvanometer shows zero deflection because no current passes through it.
If the balancing point divides the wire into two lengths l and (100 − l), then according to the Wheatstone Bridge principle,
R/X = l/(100 − l)
where,
- R = Known resistance
- X = Unknown resistance
- l = Length of wire from one end to the balance point (in cm)
🔷 6. Formula for Unknown Resistance
Ethan: Professor, how can we calculate the unknown resistance?
Professor: Rearranging the balance equation gives:
X = R(100 − l)/l
This equation is used to determine the value of the unknown resistance.
🔷 7. Why is the Wire One Meter Long?
Ethan: Professor, why is the bridge wire exactly one meter long?
Professor: A one-meter wire makes the measurement simple because the balancing length can be read directly in centimeters. Since the wire is uniform, the resistance is directly proportional to its measured length.
🔷 8. Null Deflection
Ethan: Professor, what is meant by null deflection?
Professor: Null deflection means that the galvanometer needle remains at zero, indicating that no current flows through the galvanometer.
Current through Galvanometer = 0
This indicates that the bridge has reached its balanced condition.
🔷 9. Numerical Example
Ethan: Professor, suppose the known resistance is 5 Ω and the balance point is at 40 cm. What is the unknown resistance?
Professor:
X = R(100 − l)/l
X = 5 × (60/40)
X = 7.5 Ω
🔷 10. Advantages of Meter Bridge
- Provides accurate measurement of unknown resistance.
- Simple construction and operation.
- Based on the null-deflection method, reducing measurement errors.
- Inexpensive and easy to maintain.
- Suitable for laboratory experiments.
🔷 11. Limitations of Meter Bridge
- Not suitable for very low resistances.
- Not suitable for very high resistances.
- Accuracy depends on the uniformity of the bridge wire.
- Errors may occur due to contact resistance and end resistance.
🔷 12. Applications
- Measurement of unknown electrical resistance.
- Verification of Wheatstone Bridge principle.
- Laboratory practical experiments.
- Comparison of electrical resistances.
- Calibration of resistance boxes.
🔷 13. Difference Between Wheatstone Bridge and Meter Bridge
| Wheatstone Bridge | Meter Bridge |
|---|---|
| General bridge circuit. | Practical form of Wheatstone Bridge. |
| Uses four resistors. | Uses a one-meter uniform wire. |
| Balancing is done by changing resistance values. | Balancing is done by moving the jockey. |
| Used in electrical measurements. | Mainly used in educational laboratories. |
📦 14. Important Results (Must Remember)
- Meter Bridge is based on the Wheatstone Bridge principle.
- It uses a one-meter long uniform wire.
- Resistance of the wire is proportional to its length.
- At balance, the galvanometer shows zero deflection.
- Balance condition: R/X = l/(100 − l).
- Unknown resistance: X = R(100 − l)/l.
- It is a null-deflection instrument.
- Used for accurate measurement of unknown resistance.
🧠 15. Conceptual Questions
🔹 Q1
Ethan: On which principle does the Meter Bridge work?
Professor: It works on the Wheatstone Bridge principle.
🔹 Q2
Ethan: Why is the bridge wire one meter long?
Professor: To make resistance directly proportional to the measured length and simplify calculations.
🔹 Q3
Ethan: What indicates that the bridge is balanced?
Professor: The galvanometer shows zero deflection.
🔹 Q4
Ethan: What is the role of the jockey?
Professor: It is used to locate the balance point on the bridge wire.
🔹 Q5
Ethan: Why is the Meter Bridge called a null method?
Professor: Because measurements are taken when the galvanometer current becomes zero.
🔷 16. Summary
The Meter Bridge is a practical application of the Wheatstone Bridge used for measuring unknown electrical resistance accurately. It consists of a one-meter long uniform wire, a known resistance, an unknown resistance, a galvanometer, and a jockey. At the balance point, no current flows through the galvanometer, and the unknown resistance is calculated using the ratio of the wire lengths. Owing to its simplicity, accuracy, and reliability, the Meter Bridge is one of the most widely used instruments in school and college physics laboratories.
✨ End of Topic: Meter Bridge ✨
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