Calculate the combined resistance of two or more resistors in series

4.3.2 Series and Parallel Circuits

Series Circuits – The Water‑Pipe Analogy

Think of a series circuit like a single water pipe that splits into several smaller pipes one after another. The water (current) must pass through each pipe (resistor) in turn, so the total resistance is the sum of all the individual resistances.

• All components share the same current.
• Voltage drops across each resistor add up to the total supply voltage.
• Adding more resistors always increases the total resistance.

Parallel Circuits – The Road Network Analogy

In a parallel circuit, imagine a main road that splits into several side roads. The current can choose any path, so the overall resistance is lower than any single branch. The formula for two resistors in parallel is:

$R_{\text{total}} = \dfrac{R_1 R_2}{R_1 + R_2}$

Calculating Combined Resistance in Series

1. List each resistor value: $R_1, R_2, \dots, R_n$.
2. Use the series formula:

   $R_{\text{total}} = \sum_{i=1}^{n} R_i$

3. Perform the addition carefully, checking units (ohms, Ω).
4. Verify with a calculator or a quick mental check.

Example Problem

Calculate the total resistance of the following series circuit:

Solution:

$R_{\text{total}} = 4\,\Omega + 6\,\Omega + 10\,\Omega = 20\,\Omega$