🔋 Chapter 53: Measurement of Internal Resistance of a Cell (Using Potentiometer)
🔷 1. Introduction
Every practical cell possesses an internal resistance due to the electrolyte and electrodes inside it. Whenever current flows through the cell, a part of the EMF is lost inside the cell itself because of this internal resistance.
A potentiometer provides one of the most accurate methods for measuring the internal resistance of a cell because it works on the null-deflection principle and does not draw current from the cell while measuring its EMF.
🔷 2. What is Internal Resistance?
Ethan: Professor, what is meant by the internal resistance of a cell?
Professor: Internal resistance is the resistance offered to the flow of current inside the cell by its electrolyte and electrodes.
Academic Definition
The internal resistance of a cell is the opposition offered by the electrolyte and electrodes to the flow of electric current inside the cell.
🔷 3. Principle of Measurement
Ethan: Professor, on what principle is the internal resistance measured?
Professor: The measurement is based on comparing the balancing length corresponding to the EMF of the cell with the balancing length corresponding to its terminal potential difference when the cell supplies current through a known external resistance.
Since the potential difference measured by a potentiometer is directly proportional to the balancing length,
V ∝ l
🔷 4. Experimental Procedure
Ethan: Professor, how is the experiment performed?
Professor:
- Connect the cell to the potentiometer without any external load.
- Find the balancing length l₁ corresponding to the EMF of the cell.
- Now connect a known external resistance R across the cell.
- The cell now supplies current and its terminal voltage decreases.
- Find the new balancing length l₂.
- Use these two balancing lengths to calculate the internal resistance.
🔷 5. Relation Between EMF and Terminal Voltage
Ethan: Professor, how are the balancing lengths related to the EMF and terminal voltage?
Professor: Since the potential gradient remains constant throughout the experiment,
E/V = l₁/l₂
where,
- E = EMF of the cell.
- V = Terminal potential difference.
- l₁ = Balancing length for EMF.
- l₂ = Balancing length for terminal voltage.
🔷 6. Formula for Internal Resistance
Ethan: Professor, what is the formula used to calculate the internal resistance?
Professor: If R is the known external resistance connected across the cell, then the internal resistance is given by
r = R [(l₁/l₂) − 1]
where,
- r = Internal resistance of the cell.
- R = External resistance.
- l₁ = Balancing length for EMF.
- l₂ = Balancing length for terminal voltage.
🔷 7. Why Does the Balancing Length Decrease?
Ethan: Professor, why is the second balancing length always smaller?
Professor: When the external resistance is connected, current flows through the cell. Due to the internal resistance, a part of the EMF is lost inside the cell. Therefore, the terminal potential difference becomes smaller than the EMF, resulting in a shorter balancing length.
l₂ < l₁
🔷 8. Numerical Example
Ethan: Professor, suppose the balancing length for EMF is 120 cm, the balancing length for terminal voltage is 100 cm, and the external resistance is 4 Ω. Find the internal resistance.
Professor:
Given,
l₁ = 120 cm
l₂ = 100 cm
R = 4 Ω
r = 4[(120/100) − 1]
r = 4(1.2 − 1)
r = 0.8 Ω
🔷 9. Precautions
- Keep the current through the potentiometer wire constant.
- Use a uniform potentiometer wire.
- Take accurate balancing lengths.
- Ensure proper electrical connections.
- Use a suitable external resistance.
- Avoid heating of the potentiometer wire.
🔷 10. Applications
- Measurement of internal resistance of dry cells.
- Testing rechargeable batteries.
- Laboratory experiments.
- Battery quality testing.
- Electrical instrument calibration.
📦 11. Important Results (Must Remember)
- Internal resistance exists inside every practical cell.
- Potentiometer measures internal resistance accurately because it uses the null-deflection method.
- EMF balancing length = l₁.
- Terminal voltage balancing length = l₂.
- l₂ < l₁.
- E/V = l₁/l₂.
- r = R[(l₁/l₂) − 1].
- Higher internal resistance causes a larger voltage drop inside the cell.
🧠 12. Conceptual Questions
🔹 Q1
Ethan: Why is a potentiometer used to measure internal resistance?
Professor: Because it measures voltage accurately without drawing current from the cell.
🔹 Q2
Ethan: Which balancing length is greater, l₁ or l₂?
Professor: l₁ is greater because it corresponds to the EMF of the cell.
🔹 Q3
Ethan: Why does the terminal voltage become smaller than the EMF?
Professor: Because a part of the EMF is lost across the internal resistance when current flows.
🔹 Q4
Ethan: What is the formula for internal resistance?
Professor: r = R[(l₁/l₂) − 1].
🔹 Q5
Ethan: Why should the potentiometer current remain constant?
Professor: To keep the potential gradient constant throughout the experiment.
🔷 13. Summary
The internal resistance of a cell is measured accurately using a potentiometer by comparing the balancing lengths corresponding to the EMF and the terminal potential difference of the cell. Since the potentiometer works on the null-deflection principle, it does not draw current from the cell during EMF measurement, ensuring high accuracy. The internal resistance is calculated using the relation r = R[(l₁/l₂) − 1], where R is the known external resistance and l₁ and l₂ are the balancing lengths for EMF and terminal voltage, respectively.
✨ End of Topic: Measurement of Internal Resistance of a Cell ✨
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