Kirchhoff’s Current Law (KCL): Which statement correctly expresses KCL at a circuit node (junction)?

Introduction / Context:
Kirchhoff’s Current Law is a direct statement of charge conservation at a junction. It is fundamental to nodal analysis and applies regardless of the circuit’s complexity, provided the lumped-element model is valid.

Given Data / Assumptions:

• We consider a single node (junction of elements).
• Currents are signed by direction (entering positive, leaving negative, or vice versa).
• No charge storage at the node under steady-state lumped assumptions.

Concept / Approach:
KCL states: ΣI_node = 0. Equivalently, total current entering equals total current leaving. This is a formal expression of conservation of charge—charge cannot accumulate indefinitely at a node in steady state.

Step-by-Step Solution:
Define reference directions for all branch currents at the node.Sum currents with sign according to direction.Set the algebraic sum equal to zero to form node equations.

Verification / Alternative check:
In nodal analysis, each node equation is built from KCL; solving the resulting linear system yields node voltages and branch currents, validating the law numerically in countless examples.

Why Other Options Are Wrong:
Proportional current–resistance statement: misstates Ohm’s law (current is proportional to voltage, inversely to resistance).Loop statement: belongs to KVL, not KCL.Total current less than smallest current: not a law and generally false.

Common Pitfalls:
Sign errors when summing currents; confusing node equations with loop equations; forgetting displacement current effects at very high frequencies (beyond lumped model scope).

Final Answer:
The algebraic sum of currents entering and leaving a point is equal to zero