Series-resistance rule — for ideal resistors connected in series, how is the total resistance calculated?

Introduction / Context:
Series connections appear everywhere in electronics, from simple dividers to bias networks. Knowing how to combine resistances in series enables quick current estimates and power budgeting. This item asks for the correct method to find the equivalent resistance of several resistors in series.

Given Data / Assumptions:

• Ideal resistors R1, R2, …, Rn in series.
• Single current flows through all series components.
• Standard Ohm’s law and Kirchhoff’s laws apply.

Concept / Approach:
With one common current I, each resistor drops V_k = I*R_k. The source must supply the sum of these drops, so V_total = I*(R1 + R2 + … + Rn). Therefore, the equivalent resistance is R_total = V_total / I = R1 + R2 + … + Rn. This is a direct consequence of KVL and Ohm’s law in a single-loop circuit.

Step-by-Step Solution:

Verification / Alternative check:
Measure with a bench supply: doubling one resistor doubles its portion of the drop, and the net acts like one larger resistor equal to the arithmetic sum, matching calculations and meter readings.

Why Other Options Are Wrong:

• Product over sum: That is the two-resistor parallel shortcut, not series.
• Average: Underestimates the true series equivalent.
• Reciprocal of sum of reciprocals: That is the general parallel formula.

Common Pitfalls:
Memorizing the parallel formula and misapplying it to series, or assuming averages apply because the current is common. In series, resistances add directly.

Final Answer:
Correct — add individual resistances to obtain the total series resistance.