Series circuits — as additional resistors are added in series (one after another in a single path), the total equivalent resistance of the circuit increases. Evaluate this statement for ideal resistors.

Introduction / Context:
Understanding how total resistance changes when components are added is foundational for circuit design and troubleshooting. In a series connection, components share exactly one continuous path for current. Knowing how equivalent resistance behaves helps predict changes in current, voltage division, and power dissipation when adding or removing parts.

Given Data / Assumptions:

• Ideal, linear resistors are connected strictly in series.
• Temperature effects and tolerance are ignored.
• Single DC source and steady-state conditions are assumed for intuition, though the rule is topology-based and source-agnostic.

Concept / Approach:
For resistors in series, the equivalent resistance is the arithmetic sum: R_total = R1 + R2 + … + Rn. Each added resistor contributes a positive amount of ohmic opposition to current. Therefore, adding any additional positive resistance increases R_total, which for a fixed source voltage reduces circuit current via Ohm’s law I = V/R_total.

Step-by-Step Solution:

Verification / Alternative check:
Try numbers: Two 1 kΩ resistors in series → 2 kΩ. Add 470 Ω → 2.47 kΩ. With a 10 V source, current drops from 10/2000 = 5 mA to 10/2470 ≈ 4.05 mA, consistent with increased total resistance.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing series with parallel (where adding a branch can reduce R_total); assuming physical proximity implies series—node analysis must confirm a single current path.

Final Answer:
Correct