Series resistors: What determines the total (equivalent) resistance of a series circuit containing multiple resistors?

Introduction / Context:
Total resistance in series is a foundational topic used whenever we analyze current flow, power dissipation, or voltage division across components in one path. Getting this right enables quick back-of-the-envelope calculations and safe component selection.

Given Data / Assumptions:

• Ideal resistors connected end to end (series).
• Single-path current (same current through each element).
• Ohm’s law applies: V = I * R.

Concept / Approach:
In series, each resistor drops some voltage equal to I * R_i. The source must supply the sum of all drops. Therefore the equivalent series resistance R_total is the arithmetic sum of the individual resistances: R_total = R1 + R2 + ... + Rn. This directly follows from KVL (sum of voltage rises equals sum of drops around a loop).

Step-by-Step Solution:

Verification / Alternative check:
Measure with an ohmmeter across the string: reading equals the sum of individual ohmmeter readings taken separately, confirming the additive property of series resistors.

Why Other Options Are Wrong:

• Largest/minus/smallest: These rules of thumb do not apply in series; all values contribute linearly.

Common Pitfalls:
Confusing series (add R) with parallel (add conductances). In parallel the smallest resistor dominates; in series every resistor adds to the total.

Final Answer:
the sum of the resistors