Series resistors — evaluating the claim: “Total series resistance equals the difference between largest and smallest resistor.” Is this statement true or false?

Introduction / Context:This item checks fundamental circuit theory for series connections. In series, the same current flows through each element, and resistances combine in a straightforward way. Misconceptions here can cascade into errors in power dissipation and voltage-divider design.

Given Data / Assumptions:

• N resistors R1, R2, …, RN connected in series.
• Ideal components (no temperature coefficients or parasitics considered).

Concept / Approach:The equivalent resistance of series elements is the sum of their resistances because voltage drops add while current is common: R_eq = R1 + R2 + … + RN. A “difference between largest and smallest” (R_max − R_min) ignores the contribution of intermediate elements and is physically unjustified except in trivial corner cases that still do not generalize.

Step-by-Step Solution:

Verification / Alternative check:Measure total resistance with an ohmmeter across the series string—the reading is the arithmetic sum. Kirchhoff’s Voltage Law likewise confirms additive drops around the loop.

Why Other Options Are Wrong:

• Choosing “True” contradicts both KVL and the definition of resistance in series.

Common Pitfalls:Confusing series and parallel formulas; mistakenly subtracting because voltage drops can oppose in some AC phasor contexts (which is not applicable to purely resistive DC series networks).

Final Answer:False