According to Kirchhoff's Voltage Law (KVL), which statement correctly describes the relationship of voltage rises and drops around any closed loop in a series circuit?

Introduction / Context:
Kirchhoff's laws form the backbone of circuit analysis. KVL addresses voltages around loops, while KCL addresses currents at nodes. Knowing which statement reflects KVL helps avoid mixing the two and ensures correct loop equations.

Given Data / Assumptions:

• A single closed loop that may include sources and passive elements.
• Reference polarities are chosen consistently around the loop.
• Ideal lumped elements and steady-state conditions.

Concept / Approach:
KVL states that the algebraic sum of all voltage rises and drops around a closed loop is zero. In a simple series circuit with one source, this is commonly paraphrased as: the sum of the voltage drops equals the applied source voltage, provided polarities are taken consistently.

Step-by-Step Solution:
Write the loop equation: sum of rises + sum of drops = 0.Rearrange for a single source: sum of drops = source voltage.Interpret physically: energy gained from sources is exactly lost in elements.Thus, the stated option correctly expresses KVL for a series circuit.

Verification / Alternative check:
Measure with a voltmeter across each element in a simple loop with a DC source. The measured drops add to the terminal voltage of the source, confirming KVL experimentally.

Why Other Options Are Wrong:
Resistances summing to voltages confuses units and KCL/KVL concepts.

KCL statement (sum of currents at a node equals zero) is not KVL.

Identical voltages across series elements is generally false unless impedances are equal.

Power statement is unrelated to KVL and is dimensionally inconsistent as written.

Common Pitfalls:
Sign errors when summing voltage rises and drops, and mixing KCL with KVL. Always define a direction and stick with it around the loop.

Final Answer:
the sum of the voltage drops in a series circuit is equal to the total applied voltage