Kirchhoff’s Current Law (KCL) in parallel circuits: Which statement correctly expresses the junction rule for currents at a node?

Introduction / Context:
Kirchhoff’s Current Law (KCL) is fundamental for analyzing parallel circuits, nodal voltages, and complex networks. It embodies charge conservation at a node in steady state.

Given Data / Assumptions:

• Steady-state DC (no charge accumulating at the node).
• Ideal wires and components; currents are algebraic with sign conventions.

Concept / Approach:
KCL states that the algebraic sum of currents at a node is zero. Equivalently, the sum of currents entering a node equals the sum of currents leaving that node. This is independent of the number of branches or their resistances.

Step-by-Step Reasoning:
Define current directions with signs (into node positive, out negative).Apply conservation of charge: Σ I_into − Σ I_out = 0 ⇒ Σ I_into = Σ I_out.This directly matches the correct response.

Verification / Alternative check:
In nodal analysis, each node equation enforces KCL. Solutions that violate Σ I_into = Σ I_out indicate modeling or calculation errors.

Why Other Options Are Wrong:
Option (a) resembles Kirchhoff’s Voltage Law (KVL), not KCL. Option (b) is a property of parallel resistors, not a current law. Option (c) misstates the equality with a “difference.”

Common Pitfalls:
Mixing KCL and KVL statements or forgetting to keep a consistent current sign convention.

Final Answer:
sum of the total currents flowing out of a junction equals the sum of the total currents flowing into that junction