Series voltage division: In a series circuit, two resistors show equal voltage drops. What does this indicate about the resistor values?

Introduction / Context:
Voltage division in a series string distributes the source voltage in proportion to the resistances. Observing equal drops can be used as a diagnostic to infer component equality or to spot faults in measurement setups.

Given Data / Assumptions:

• Two resistors in series with the same current flowing through each.
• Measured voltage drops across each resistor are equal.
• Resistors are ideal (no tolerance or temperature effects considered).

Concept / Approach:
In series, V_i = I * R_i. With the same current I through both, equality of voltages implies equality of resistances: V1 = V2 ⇒ IR1 = IR2 ⇒ R1 = R2. Therefore identical voltage drops indicate equal resistor values (within measurement accuracy).

Step-by-Step Solution:

Verification / Alternative check:
Swap the positions of the resistors; equal drops will persist if their values are equal, confirming the inference.

Why Other Options Are Wrong:

• Parallel: Not applicable; the circuit is series.
• Unequal value / voltage doubled: Both contradict the given equal drops and series current rule.

Common Pitfalls:
Overlooking meter loading or tolerance; in real labs, small differences may exist due to 1–5% tolerance parts.

Final Answer:
they are of equal value