Series circuit with unequal resistors: Which statement is NOT true for a series network containing resistors of different values?

Introduction:
Series circuits are ubiquitous, and their rules are foundational. With unequal resistor values, some properties remain universally true while others do not. Distinguishing these clarifies voltage division and current continuity in basic circuit analysis.

Given Data / Assumptions:

• Resistors are connected in a single series path.
• Values are different (R1 ≠ R2 ≠ …).
• Steady DC conditions (no reactive effects).

Concept / Approach:

Key series properties: the same current flows through every element; total resistance equals the arithmetic sum of individual resistances; and the source voltage equals the sum of all individual voltage drops (Kirchhoff's Voltage Law). However, the individual voltage drops are proportional to resistance values and therefore are generally not equal when resistances differ.

Step-by-Step Solution:

Verification / Alternative check:

Example: Two series resistors 1 kΩ and 2 kΩ on 9 V produce voltage drops 3 V and 6 V, confirming unequal drops proportional to resistance.

Why Other Options Are Wrong:

• The current through each resistor is the same: True by series continuity.
• The sum of the voltage drops will be equal (to the source): Interpreted with KVL, this is true.
• The total resistance is the sum of values: True for series elements.
• The source voltage equals the sum of drops: Restates KVL, true.

Common Pitfalls:

• Misreading a vague statement about 'sum of drops'; always tie it to KVL and the source voltage.
• Assuming identical voltage drops without checking resistor values.

Final Answer:

The voltage drop across each resistor is the same.