🔋 Chapter 48: Combination of Cells in Series (Class XII)
🔷 1. Introduction
Many electrical devices require a voltage greater than that supplied by a single cell. In such situations, two or more cells are connected together to form a battery. One of the simplest methods of connecting cells is the series combination.
In a series combination, the positive terminal of one cell is connected to the negative terminal of the next cell. This arrangement increases the total electromotive force (EMF) of the battery.
🔷 2. What is a Series Combination of Cells?
Ethan: Professor, what is meant by connecting cells in series?
Professor: When the positive terminal of one cell is connected to the negative terminal of the next cell, the cells are said to be connected in series.
Academic Definition
A series combination of cells is an arrangement in which the positive terminal of one cell is connected to the negative terminal of the next cell so that the total EMF becomes the algebraic sum of the individual EMFs.
🔷 3. Purpose of Connecting Cells in Series
Ethan: Professor, why are cells connected in series?
Professor: Cells are connected in series when a higher voltage is required than can be supplied by a single cell.
- To increase the total EMF.
- To operate high-voltage electrical devices.
- To supply larger potential differences to a circuit.
🔷 4. Total EMF of Cells Connected in Series
Ethan: Professor, how do we calculate the total EMF?
Professor: The total EMF is the sum of the EMFs of all the cells connected in series.
E = E₁ + E₂ + E₃ + ⋯
If all the cells are identical and each has an EMF E, then
Total EMF = nE
where,
- n = Number of cells
- E = EMF of one cell
🔷 5. Total Internal Resistance
Ethan: Professor, what happens to the internal resistance?
Professor: The internal resistances of all the cells are also added together.
r = r₁ + r₂ + r₃ + ⋯
For identical cells,
Total Internal Resistance = nr
🔷 6. Current Supplied by the Battery
Ethan: Professor, how do we calculate the current supplied by the battery?
Professor: If an external resistance R is connected to the battery, then the current is given by:
I = nE / (R + nr)
where,
- I = Current supplied by the battery
- nE = Total EMF
- R = External resistance
- nr = Total internal resistance
🔷 7. Terminal Potential Difference
Ethan: Professor, what is the terminal voltage of the battery?
Professor: The terminal potential difference is the voltage available across the external circuit.
V = nE − I(nr)
🔷 8. Special Cases
Ethan: Professor, when is a series combination most useful?
Professor:
- When a high voltage is required.
- When the external resistance is much larger than the internal resistance of the battery.
- Examples include flashlights, emergency lamps, and battery-operated devices.
🔷 9. Advantages of Series Combination
- Provides higher EMF.
- Simple electrical connection.
- Suitable for high-voltage applications.
- Widely used in portable electrical devices.
🔷 10. Disadvantages of Series Combination
- Total internal resistance increases.
- If one cell becomes defective, the entire battery performance is affected.
- Not suitable when very large currents are required.
🔷 11. Numerical Example
Ethan: Professor, four identical cells each having an EMF of 1.5 V and internal resistance of 0.5 Ω are connected in series. They are connected to an external resistance of 8 Ω. Find the current.
Professor:
Total EMF = 4 × 1.5 = 6 V
Total Internal Resistance = 4 × 0.5 = 2 Ω
I = 6 / (8 + 2)
I = 0.6 A
🔷 12. Applications
- Flashlights (torches).
- Remote controls.
- Battery-powered toys.
- Portable radios.
- Emergency lighting systems.
- Electronic measuring instruments.
📦 13. Important Results (Must Remember)
- In series, the positive terminal of one cell is connected to the negative terminal of the next.
- Total EMF = Sum of individual EMFs.
- For identical cells, Total EMF = nE.
- Total internal resistance = Sum of individual internal resistances.
- For identical cells, Total internal resistance = nr.
- Current supplied: I = nE/(R + nr).
- Terminal voltage: V = nE − I(nr).
- Series combination is preferred when higher voltage is required.
🧠 14. Conceptual Questions
🔹 Q1
Ethan: Why are cells connected in series?
Professor: To obtain a higher EMF or higher voltage.
🔹 Q2
Ethan: What happens to the total EMF in a series combination?
Professor: It becomes the sum of the individual EMFs.
🔹 Q3
Ethan: What happens to the internal resistance?
Professor: The internal resistances are added together.
🔹 Q4
Ethan: When is a series combination most suitable?
Professor: When high voltage and relatively small current are required.
🔹 Q5
Ethan: What is the total EMF of six identical cells each having an EMF of 2 V?
Professor: Total EMF = 6 × 2 = 12 V.
🔷 15. Summary
In a series combination, the positive terminal of one cell is connected to the negative terminal of the next cell. The total EMF of the battery is equal to the sum of the individual EMFs, while the total internal resistance is also the sum of the individual internal resistances. This arrangement is used whenever a higher voltage is required. The current supplied by the battery depends on the total EMF, total internal resistance, and the external resistance connected to the circuit.
✨ End of Topic: Combination of Cells in Series ✨
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