⚡ Chapter 52: Measurement of Small Resistances (Class XII)
🔷 1. Introduction
The measurement of small resistances is an important topic in electrical measurements. Ordinary methods such as Ohm's law are not suitable for measuring very small resistances because the resistance of connecting wires and contact points becomes comparable to the resistance being measured, resulting in significant errors.
Therefore, special methods such as the Potentiometer Method, Carey Foster Bridge, and Kelvin Double Bridge are used to obtain accurate measurements of low resistances.
🔷 2. Why is Measuring Small Resistance Difficult?
Ethan: Professor, why can't we measure very small resistance using an ordinary ohmmeter?
Professor: Because the resistance of connecting wires, contacts, and instrument leads becomes comparable to the unknown resistance. These additional resistances introduce large errors in the measurement.
Important Observation
For very small resistances, the resistance of leads and contact points cannot be neglected.
🔷 3. Characteristics of Small Resistances
Ethan: Professor, what values are generally considered small resistances?
Professor: Resistances ranging from a few milliohms (mΩ) to a few ohms are generally treated as small resistances in electrical measurements.
- Very small voltage drop across the resistor.
- Large current is required for accurate measurement.
- Lead resistance affects the result.
- High precision instruments are required.
🔷 4. Potentiometer Method
Ethan: Professor, how can a potentiometer measure a small resistance?
Professor: A known current is passed through the unknown resistor, and the very small potential difference across it is measured accurately using a potentiometer. The resistance is then calculated using Ohm's law.
R = V/I
where,
- R = Unknown resistance.
- V = Potential difference measured by the potentiometer.
- I = Current flowing through the resistor.
🔷 5. Carey Foster Bridge
Ethan: Professor, what is the Carey Foster Bridge?
Professor: The Carey Foster Bridge is a modified Wheatstone Bridge specially designed for comparing two nearly equal small resistances with very high accuracy.
- Measures the difference between two nearly equal resistances.
- Eliminates errors due to lead resistance.
- Commonly used in precision laboratories.
🔷 6. Kelvin Double Bridge
Ethan: Professor, what is the Kelvin Double Bridge?
Professor: The Kelvin Double Bridge is an improved form of the Wheatstone Bridge that eliminates errors caused by connecting leads and contact resistances. It is the most accurate method for measuring extremely small resistances.
- Used for milliohm measurements.
- Removes lead resistance error.
- Highly accurate.
- Widely used in industries and laboratories.
🔷 7. Sources of Error
Ethan: Professor, what causes errors while measuring small resistances?
Professor:
- Resistance of connecting wires.
- Contact resistance.
- Temperature rise due to heating.
- Poor electrical connections.
- Instrument calibration errors.
🔷 8. Precautions
Ethan: Professor, what precautions should we take?
Professor:
- Use thick, low-resistance connecting wires.
- Ensure tight electrical contacts.
- Avoid excessive current to prevent heating.
- Use calibrated instruments.
- Maintain constant temperature during measurement.
🔷 9. Applications
- Measurement of transformer winding resistance.
- Testing electrical cables.
- Measurement of bus-bar resistance.
- Testing electrical contacts and switches.
- Measurement of shunt resistors.
- Industrial quality control.
📦 10. Important Results (Must Remember)
- Ordinary Ohm's law method is not sufficiently accurate for very small resistances.
- Lead resistance and contact resistance introduce significant errors.
- Potentiometer measures the small potential difference accurately.
- Resistance is calculated using R = V/I.
- Carey Foster Bridge compares two nearly equal small resistances.
- Kelvin Double Bridge is the most accurate method for measuring very small resistances.
- Temperature should remain constant during measurement.
- Good electrical contacts improve measurement accuracy.
🧠 11. Conceptual Questions
🔹 Q1
Ethan: Why is measuring small resistance difficult?
Professor: Because lead resistance and contact resistance become comparable to the resistance being measured.
🔹 Q2
Ethan: Which formula is used when measuring small resistance using a potentiometer?
Professor: R = V/I.
🔹 Q3
Ethan: Which bridge is specially designed to measure very small resistances?
Professor: Kelvin Double Bridge.
🔹 Q4
Ethan: Why is the Carey Foster Bridge used?
Professor: It accurately compares two nearly equal small resistances.
🔹 Q5
Ethan: Why should temperature remain constant during measurement?
Professor: Because resistance changes with temperature, affecting the accuracy of the measurement.
🔷 12. Summary
The measurement of small resistances requires special techniques because lead resistance and contact resistance can introduce significant errors. Accurate methods such as the potentiometer method, Carey Foster Bridge, and Kelvin Double Bridge are used to overcome these errors. Among these, the Kelvin Double Bridge is the most accurate method for measuring very low resistances. Proper electrical connections, calibrated instruments, and constant temperature are essential for obtaining precise measurements.
✨ End of Topic: Measurement of Small Resistances ✨
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