Kirchhoff’s Voltage Law (KVL): Which statement correctly expresses KVL for any closed loop in an electrical network?

Introduction / Context:
Kirchhoff’s laws are foundational for circuit analysis. Kirchhoff’s Voltage Law (KVL) applies energy conservation to a closed loop: as you traverse a loop, rises and drops in potential must balance out to zero. This law is independent of component details and holds for lumped, time-invariant circuits.

Given Data / Assumptions:

• We consider closed loops in a lumped circuit.
• Voltages are taken with sign (algebraic sum).
• Steady-state or quasi-static conditions where lumped-parameter assumptions are valid.

Concept / Approach:
KVL states: ΣV_loop = 0. Practically, the sum of source rises equals the sum of component drops around any loop. This is a direct application of energy conservation—returning to the starting node leaves net energy change at zero.

Step-by-Step Solution:
Define a loop and a traversal direction.Add signed voltage rises and drops encountered.Set the algebraic sum equal to zero: ΣV = 0.Use this to solve for unknown voltages or currents via Ohm’s law relationships.

Verification / Alternative check:
Apply to a simple source-resistor loop: V_source − I*R = 0 ⇒ I = V_source / R, which matches Ohm’s law.

Why Other Options Are Wrong:
Parallel circuit statement: unrelated to KVL and not generally true.Proportional voltage drop: this is Ohm’s law, not KVL.Node statement: that is Kirchhoff’s Current Law (KCL), not KVL.

Common Pitfalls:
Mixing KVL and KCL; neglecting polarity when summing voltages; forgetting that induced emf or time-varying fields can require careful treatment.

Final Answer:
The algebraic sum of voltages in a loop is equal to zero