Series Combination of Resistors

Definition

When resistors are connected end-to-end such that the same current flows through each of them, they are said to be connected in series.

Characteristics

  • Same current flows through all resistors.
  • The total voltage across the combination is equal to the sum of voltages across individual resistors.
  • Total resistance increases with more resistors.

Diagram

(Insert image: battery connected to R1, R2, R3 in series)

Derivation

Let resistors \( R_1, R_2, R_3 \) be connected in series. Let the current flowing be \( I \). Voltage drops across each resistor:

\[ V_1 = I R_1, \quad V_2 = I R_2, \quad V_3 = I R_3 \]

Total voltage: \[ V = V_1 + V_2 + V_3 = I(R_1 + R_2 + R_3) \]

Let \( R_s \) be the equivalent resistance: \[ V = I R_s \Rightarrow R_s = R_1 + R_2 + R_3 \]

General Formula:

For \( n \) resistors: \[ R_s = R_1 + R_2 + R_3 + \cdots + R_n \]

Conclusion

In a series circuit, the total resistance is the sum of individual resistances. The current is the same through all components, but voltage divides among them.

📘 Short Questions and Answers

  1. Q: What is a series combination of resistors?
    A: A combination in which resistors are connected end-to-end and the same current flows through all resistors.
  2. Q: Why does the current remain the same in series?
    A: Because there is only one path for current, it must be equal through each resistor.
  3. Q: How is the total resistance calculated in a series combination?
    A: By adding all the resistors: \( R_s = R_1 + R_2 + R_3 + \cdots \)
  4. Q: If three resistors of 2Ω, 3Ω, and 5Ω are in series, what is the total resistance?
    A: \( R_s = 2 + 3 + 5 = 10\,\Omega \)
  5. Q: What happens to the current if more resistors are added in series?
    A: Total resistance increases, so the current decreases for a fixed voltage.
  6. Q: What happens to the voltage across resistors in a series combination?
    A: It divides among the resistors in proportion to their resistances.