Voltage divider check — a series circuit with three resistors R1, R2, and R3 across a 55 V ideal source is measured to have drops VR1 = 10 V, VR2 = 15 V, and VR3 = 30 V. Do these readings satisfy Kirchhoff’s Voltage Law for the loop?

Introduction / Context:Voltage-divider measurements in series circuits must obey Kirchhoff’s Voltage Law (KVL): the sum of drops equals the source. This problem checks whether provided voltage readings are self-consistent for a loop driven by an ideal 55 V source.

Given Data / Assumptions:

• Ideal source of 55 V and ideal wiring.
• Three resistors in strict series; no parallel branches.
• Measured drops: 10 V, 15 V, 30 V across R1, R2, R3.

Concept / Approach:Apply KVL around the loop. If the algebraic sum of measured drops equals the source magnitude, the readings are consistent with KVL. Individual resistor values are not necessary to verify the law; only the sum matters for the loop equation.

Step-by-Step Solution:

Verification / Alternative check:Using voltage division, Vi = (Ri / ΣR) * V_S. For any positive resistances that sum to ΣR, the drops will sum to V_S by construction. The exact Ri values are not needed to validate KVL compliance.

Why Other Options Are Wrong:

Common Pitfalls:Forgetting to include the source’s internal resistance drop when modeling non-ideal sources; misreading meter polarities leading to sign errors.

Final Answer:Correct — the readings satisfy KVL