🔋 Chapter 49: Combination of Cells in Parallel (Class XII)
🔷 1. Introduction
Sometimes an electrical circuit requires a large current rather than a high voltage. In such cases, connecting cells in series is not the best choice because the internal resistance also increases. Instead, the cells are connected in parallel.
In a parallel combination, all the positive terminals of the cells are connected together, and all the negative terminals are connected together. This arrangement reduces the effective internal resistance of the battery, allowing it to supply a larger current.
🔷 2. What is a Parallel Combination of Cells?
Ethan: Professor, what is meant by connecting cells in parallel?
Professor: When all the positive terminals of the cells are connected together and all the negative terminals are connected together, the cells are said to be connected in parallel.
Academic Definition
A parallel combination of cells is an arrangement in which all the positive terminals are connected together and all the negative terminals are connected together so that the effective internal resistance decreases while the EMF remains the same (for identical cells).
🔷 3. Purpose of Connecting Cells in Parallel
Ethan: Professor, why are cells connected in parallel?
Professor: Cells are connected in parallel when a larger current is required without increasing the voltage.
- To decrease the effective internal resistance.
- To increase the current supplied by the battery.
- To improve battery life.
- To maintain nearly constant voltage.
🔷 4. Effective EMF of Cells in Parallel
Ethan: Professor, what is the effective EMF of identical cells connected in parallel?
Professor: For identical cells having the same EMF, the effective EMF of the combination remains equal to the EMF of one cell.
Effective EMF = E
where,
- E = EMF of one cell.
🔷 5. Effective Internal Resistance
Ethan: Professor, what happens to the internal resistance when identical cells are connected in parallel?
Professor: The effective internal resistance decreases because the internal resistances are connected in parallel.
Effective Internal Resistance = r/n
where,
- r = Internal resistance of one cell.
- n = Number of identical cells.
🔷 6. Current Supplied by the Battery
Ethan: Professor, how do we calculate the current supplied by cells connected in parallel?
Professor: If an external resistance R is connected across the battery, the current supplied is
I = E / (R + r/n)
where,
- E = EMF of one cell.
- R = External resistance.
- r/n = Effective internal resistance.
🔷 7. Terminal Potential Difference
Ethan: Professor, what is the terminal voltage of the parallel combination?
Professor: The terminal potential difference is given by
V = E − I(r/n)
This is the voltage available across the external circuit.
🔷 8. Condition for Maximum Advantage
Ethan: Professor, when is a parallel combination preferred over a series combination?
Professor: A parallel combination is preferred when the external resistance is small compared to the internal resistance of a single cell. The reduced effective internal resistance allows the battery to deliver a larger current efficiently.
Preferred when R is small.
🔷 9. Advantages of Parallel Combination
- Effective internal resistance decreases.
- Larger current can be supplied.
- Battery lasts longer because the load is shared.
- Suitable for low-resistance circuits.
- The voltage remains equal to that of one cell (for identical cells).
🔷 10. Disadvantages of Parallel Combination
- The voltage cannot be increased.
- All cells should have nearly the same EMF.
- If cells have different EMFs, unwanted circulating currents may flow.
- Requires proper matching of identical cells.
🔷 11. Numerical Example
Ethan: Professor, four identical cells each have an EMF of 2 V and an internal resistance of 1 Ω. They are connected in parallel to an external resistance of 3 Ω. Find the current supplied.
Professor:
Effective EMF = 2 V
Effective Internal Resistance = 1/4 = 0.25 Ω
I = 2 / (3 + 0.25)
I = 0.615 A (approximately)
🔷 12. Applications
- Automobile batteries.
- Emergency power supplies.
- Solar battery banks.
- Power backup systems.
- Portable power stations.
- High-current electrical equipment.
📦 13. Important Results (Must Remember)
- In parallel, all positive terminals are connected together and all negative terminals are connected together.
- For identical cells, Effective EMF = E.
- Effective internal resistance = r/n.
- Current supplied: I = E/(R + r/n).
- Terminal voltage: V = E − I(r/n).
- Parallel combination is preferred when a large current is required.
- It reduces the effective internal resistance of the battery.
- It is suitable for circuits having low external resistance.
🧠 14. Conceptual Questions
🔹 Q1
Ethan: Why are cells connected in parallel?
Professor: To reduce the effective internal resistance and supply a larger current.
🔹 Q2
Ethan: What is the effective EMF of identical cells connected in parallel?
Professor: It is equal to the EMF of one cell.
🔹 Q3
Ethan: What happens to the internal resistance in a parallel combination?
Professor: It decreases to r/n for n identical cells.
🔹 Q4
Ethan: When is a parallel combination preferred?
Professor: When a large current is required and the external resistance is small.
🔹 Q5
Ethan: Can a parallel combination increase the voltage of the battery?
Professor: No. For identical cells, the voltage remains equal to the EMF of a single cell.
🔷 15. Summary
In a parallel combination, all the positive terminals of the cells are connected together, and all the negative terminals are connected together. For identical cells, the effective EMF remains equal to the EMF of one cell, while the effective internal resistance decreases to r/n. As a result, the battery can supply a larger current without increasing the voltage. This arrangement is most suitable for low-resistance circuits where high current and longer battery life are required.
✨ End of Topic: Combination of Cells in Parallel ✨
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