Kirchhoff’s Voltage Law (KVL) in series loops — the sum of all individual voltage drops around a series circuit equals the source voltage. Assess this statement for ideal components.

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
Kirchhoff’s Voltage Law is a cornerstone of circuit analysis. It expresses energy conservation around a closed path: the total rise from sources equals the total drop across elements. In series circuits, this means the source voltage is apportioned among the series elements according to their impedances.


Given Data / Assumptions:

  • Ideal wiring and components (no parasitic EMF sources).
  • Closed single-loop series circuit.
  • Steady-state analysis for simplicity; KVL is general and also applies instantaneously in AC.


Concept / Approach:
KVL states ΣV_rises − ΣV_drops = 0. For a single source V_S and series elements with drops V1, V2, …, Vn, we have V_S = V1 + V2 + … + Vn. This enables voltage-divider design and power budgeting in series networks.


Step-by-Step Solution:

Define loop direction and label polarities using the passive sign convention.Write KVL: +V_S − V1 − V2 − … − Vn = 0.Rearrange: V_S = V1 + V2 + … + Vn.Use Ohm’s law as needed: Vi = I * Ri, where I is the common series current.


Verification / Alternative check:
Measure all individual drops and sum them; the total equals the measured source voltage within meter tolerance. SPICE simulations enforce KVL numerically, providing another check.


Why Other Options Are Wrong:

“Incorrect” and conditional options contradict a fundamental conservation law; equality of resistances, frequency, or waveform type does not invalidate KVL for lumped circuits.


Common Pitfalls:
Mixing source internal resistance into “external” drops without accounting for it; mislabeling polarities and signs; assuming wiring is ideal while significant wiring drops exist in high-current layouts.


Final Answer:
Correct

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