⚡ Chapter 40: Series Combination of Resistors (Class XII)
🔷 1. Introduction
In an electrical circuit, two or more resistors can be connected together in different ways. One of the simplest methods is the Series Combination of Resistors.
In a series combination, resistors are connected one after another so that there is only one path available for the flow of electric current. Consequently, the same current passes through every resistor in the circuit.
🔷 2. What is a Series Combination?
Ethan: Professor, what is meant by a series combination of resistors?
Professor: A series combination is an arrangement in which resistors are connected end-to-end so that electric current has only one continuous path to follow.
Academic Definition
A series combination of resistors is an arrangement in which resistors are connected one after another in such a way that the same electric current flows through each resistor.
🔷 3. Characteristics of Series Combination
Ethan: Professor, what are the main characteristics of a series circuit?
Professor: A series circuit has the following characteristics.
- There is only one path for current.
- The same current flows through every resistor.
- The supply voltage is divided among the resistors.
- The equivalent resistance is greater than any individual resistor.
- If one resistor breaks, the entire circuit stops working.
🔷 4. Current in Series Combination
Ethan: Professor, does the current change from one resistor to another?
Professor: No. Since there is only one path available, the same current flows through every resistor.
I = I₁ = I₂ = I₃ = ···
🔷 5. Potential Difference in Series Combination
Ethan: Professor, how is the battery voltage distributed?
Professor: The total potential difference supplied by the battery is shared among all the resistors.
V = V₁ + V₂ + V₃ + ···
Each resistor receives a portion of the total voltage depending on its resistance.
🔷 6. Derivation of Equivalent Resistance
Ethan: Professor, how do we obtain the equivalent resistance of resistors connected in series?
Professor: Let three resistors R₁, R₂ and R₃ be connected in series.
Applying Ohm's Law,
V = IR
For individual resistors,
V₁ = IR₁
V₂ = IR₂
V₃ = IR₃
Since,
V = V₁ + V₂ + V₃
Substituting,
IR = IR₁ + IR₂ + IR₃
Dividing both sides by I,
R = R₁ + R₂ + R₃
For n resistors,
Req = R₁ + R₂ + R₃ + ··· + Rn
🔷 7. Physical Meaning of Series Combination
Ethan: Professor, why does the total resistance increase when resistors are connected in series?
Professor: Each resistor opposes the flow of electric current. As current passes through one resistor after another, every resistor adds its own opposition. Therefore, the total resistance becomes the sum of all individual resistances.
🔷 8. Example
Ethan: Professor, suppose three resistors of 2 Ω, 3 Ω and 5 Ω are connected in series. What is their equivalent resistance?
Professor:
R = 2 + 3 + 5
R = 10 Ω
🔷 9. Advantages of Series Combination
- Simple circuit design.
- Easy to calculate equivalent resistance.
- Same current flows through every component.
- Useful where identical current is required.
🔷 10. Disadvantages of Series Combination
- If one resistor fails, the entire circuit stops working.
- Voltage is divided among the resistors.
- Total resistance increases.
- Current decreases as more resistors are added.
🔷 11. Applications
- Decorative light strings (older designs).
- Current limiting circuits.
- Voltage divider networks.
- Laboratory resistor combinations.
- Electrical measurement circuits.
📦 12. Important Results (Must Remember)
- There is only one path for current.
- Current remains the same through every resistor.
- Total voltage equals the sum of individual voltage drops.
- Equivalent resistance is the sum of all resistances.
- Equivalent resistance is always greater than the largest individual resistance.
- If one resistor breaks, the entire circuit becomes open.
- Adding more resistors in series increases total resistance.
🧠 13. Conceptual Questions
🔹 Q1
Ethan: Why is the current the same through all resistors connected in series?
Professor: Because there is only one path available for the flow of electric current.
🔹 Q2
Ethan: How is the total voltage distributed in a series circuit?
Professor: It is divided among all the resistors, and the sum of the voltage drops equals the supply voltage.
🔹 Q3
Ethan: What is the equivalent resistance of resistors connected in series?
Professor: It is the sum of all individual resistances.
🔹 Q4
Ethan: What happens if one resistor breaks in a series circuit?
Professor: The circuit becomes open, and current stops flowing through all components.
🔹 Q5
Ethan: Is the equivalent resistance greater or smaller than the individual resistances?
Professor: It is always greater than any individual resistor in the series combination.
🔷 14. Summary
In a series combination, resistors are connected end-to-end, providing only one path for the flow of electric current. Therefore, the same current passes through every resistor, while the applied voltage is divided among them. The equivalent resistance is equal to the sum of all individual resistances, making the total resistance greater than any single resistor. Series combinations are widely used in current-limiting circuits, voltage dividers, and many electrical and electronic applications.
✨ End of Topic: Series Combination of Resistors ✨
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