🔋 Chapter 47: Internal Resistance of a Cell (Class XII)
🔷 1. Introduction
An ideal cell supplies all of its electrical energy to the external circuit. However, real cells are not ideal. Every practical cell has some resistance inside it due to its electrolyte, electrodes, and internal construction. This resistance opposes the flow of current inside the cell and is known as the Internal Resistance of the cell.
Internal resistance plays an important role in determining the current supplied by a cell and the terminal potential difference across its terminals.
🔷 2. What is Internal Resistance?
Ethan: Professor, what is internal resistance?
Professor: Internal resistance is the resistance offered to the flow of electric current inside the cell itself.
Academic Definition
The resistance offered by the electrolyte, electrodes, and other internal parts of a cell to the flow of electric current is called the internal resistance of the cell.
It is represented by the symbol r and its SI unit is ohm (Ω).
🔷 3. Why Does a Cell Have Internal Resistance?
Ethan: Professor, why does a cell have resistance inside it?
Professor: Inside a cell, electric current flows through the electrolyte by the movement of ions. These ions experience collisions with the molecules of the electrolyte and the electrodes. This opposition to the movement of charge gives rise to internal resistance.
🔷 4. Causes of Internal Resistance
Ethan: Professor, what factors cause internal resistance?
Professor: Internal resistance depends on several physical factors.
- Nature of the electrolyte.
- Concentration of the electrolyte.
- Distance between the electrodes.
- Area of the electrodes immersed in the electrolyte.
- Temperature of the electrolyte.
- Age and condition of the cell.
🔷 5. Factors Affecting Internal Resistance
| Factor | Effect on Internal Resistance |
|---|---|
| Distance between electrodes increases | Internal resistance increases. |
| Electrode area increases | Internal resistance decreases. |
| Electrolyte concentration increases | Internal resistance decreases. |
| Temperature increases | Internal resistance generally decreases. |
| Cell becomes old | Internal resistance increases. |
🔷 6. Relation Between EMF, Terminal Voltage and Internal Resistance
Ethan: Professor, how are EMF, terminal voltage and internal resistance related?
Professor: When current flows through the cell, part of the EMF is used to overcome the internal resistance of the cell.
E = V + Ir
or,
V = E − Ir
where,
- E = EMF of the cell
- V = Terminal potential difference
- I = Current through the circuit
- r = Internal resistance
🔷 7. Physical Meaning of the Equation
Ethan: Professor, what does the term Ir represent?
Professor: The quantity Ir is called the internal voltage drop. It represents the voltage lost inside the cell due to its internal resistance.
Internal Voltage Drop = Ir
🔷 8. Open Circuit Condition
Ethan: Professor, what happens when no current is drawn from the cell?
Professor: In an open circuit, no current flows.
I = 0
Therefore,
V = E
Thus, the terminal voltage is equal to the EMF of the cell.
🔷 9. Closed Circuit Condition
Ethan: Professor, what happens when the cell supplies current?
Professor: When current flows through the circuit, a voltage drop occurs across the internal resistance. Hence, the terminal voltage becomes smaller than the EMF.
Terminal Voltage < EMF
🔷 10. Numerical Example
Ethan: Professor, a cell has an EMF of 2 V and an internal resistance of 0.5 Ω. If it supplies a current of 1 A, what is its terminal voltage?
Professor:
V = E − Ir
V = 2 − (1 × 0.5)
V = 1.5 V
🔷 11. How Can Internal Resistance be Reduced?
Ethan: Professor, how can the internal resistance of a cell be reduced?
Professor: It can be reduced by improving the movement of ions inside the electrolyte.
- Using a highly conducting electrolyte.
- Increasing the concentration of the electrolyte.
- Increasing the electrode area.
- Reducing the distance between electrodes.
- Maintaining an appropriate operating temperature.
🔷 12. Applications
- Design of batteries.
- Electric vehicles.
- Mobile phone batteries.
- UPS and inverter systems.
- Power supply design.
- Battery performance analysis.
📦 13. Important Results (Must Remember)
- Internal resistance is represented by r.
- Its SI unit is ohm (Ω).
- It is caused by the resistance of the electrolyte and electrodes.
- It opposes current inside the cell.
- Internal voltage drop = Ir.
- EMF equation: E = V + Ir.
- Terminal voltage equation: V = E − Ir.
- For an open circuit, V = E.
- When current flows, terminal voltage is less than EMF.
🧠 14. Conceptual Questions
🔹 Q1
Ethan: What is internal resistance?
Professor: It is the resistance offered by the cell itself to the flow of electric current.
🔹 Q2
Ethan: Why is terminal voltage less than EMF?
Professor: Because some voltage is lost inside the cell across its internal resistance.
🔹 Q3
Ethan: What is the SI unit of internal resistance?
Professor: Ohm (Ω).
🔹 Q4
Ethan: What does Ir represent?
Professor: The voltage drop inside the cell due to internal resistance.
🔹 Q5
Ethan: Under what condition is the terminal voltage equal to the EMF?
Professor: When no current flows through the cell (open circuit).
🔷 15. Summary
Every practical cell possesses an internal resistance that opposes the flow of current inside the cell. This resistance arises from the electrolyte, electrodes, and internal structure of the cell. When the cell supplies current, a voltage drop Ir occurs inside the cell, reducing the terminal potential difference. The relation E = V + Ir explains the connection between EMF, terminal voltage, and internal resistance. Understanding internal resistance is essential for analyzing the performance and efficiency of electrical cells and batteries.
✨ End of Topic: Internal Resistance of a Cell ✨
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