Resistors in Series and Parallel
Understanding how resistors combine in circuits is essential for calculating total resistance, current flow, and voltage drops. Resistors can be connected in series, parallel, or a combination of both.
Resistors in Series
In a series circuit, resistors are connected end-to-end. The same current flows through each resistor, and the total resistance increases.
Formula:
Rtotal = R₁ + R₂ + R₃ + ...
Example:
Three resistors (4 Ω, 6 Ω, 10 Ω) are connected in series. What is the total resistance?
Calculation: Rtotal = 4 + 6 + 10 = 20 Ω
Answer: Total resistance is 20 ohms.
Resistors in Parallel
In a parallel circuit, resistors are connected across the same two points. The voltage is the same across each branch, and the total resistance is always less than the smallest resistor.
Formula (two resistors):
Rtotal = (R₁ × R₂) / (R₁ + R₂)
Formula (general case):
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...
Example:
Two resistors (6 Ω and 3 Ω) are connected in parallel. What is the total resistance?
Calculation: Rtotal = (6 × 3) / (6 + 3) = 18 / 9 = 2 Ω
Answer: Total resistance is 2 ohms.
Why It Matters
- Series increases resistance — good for limiting current.
- Parallel decreases resistance — good for sharing load.
- Knowing how to simplify helps when analyzing circuits using Ohm’s or Kirchhoff’s Laws.