Kirchhoff’s Current Law is based on the fact that

Question

BlackTom AI · Accepted Answer

Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents entering and leaving a node is zero, because charge cannot accumulate at an ideal circuit node.

Relevant concepts:
- Conservation of electric charge: charge cannot be created or destroyed in a closed region.
- Definition of node in lumped-circuit theory: a point where two or more circuit elements join, assumed to have negligible volume and no net charge storage.
- Relationship between current and charge: i = dQ/dt.

Step-by-step reasoning:
1. Let Q(t) be the net charge at a node. Currents entering the node change Q according to dQ/dt = Σ i_k (taking entering currents as positive and leaving as negative).
2. For KCL to hold in the usual lumped-circuit sense, the node does not accumulate net charge, so dQ/dt = 0.
3. Setting dQ/dt = 0 gives Σ i_k = 0 — the sum of currents into the node equals zero (or sum of currents entering = sum of currents leaving).

Illustrative calculation:
- If i1 and i2 enter the node and i3 leaves, using signs: i1 + i2 − i3 = dQ/dt.
- With no accumulation, dQ/dt = 0, so i1 + i2 − i3 = 0 → i1 + i2 = i3.

Why the correct answer is correct:
Option c, “There cannot be an accumulation of charge at a node,” is the direct physical basis of KCL: enforcing dQ/dt = 0 leads to Σ i = 0.

Why the other options are incorrect:
- a (“Charge accumulation may or may not be possible”) is vague and contradicts the strict KCL assumption of no accumulation.
- b (“Charge accumulation is possible at node”) contradicts the conservation premise used in KCL for lumped circuits.
- d (“There is a possibility for a node to store energy”) confuses nodes with elements; nodes themselves don’t store energy—energy storage occurs in capacitors/inductors, which are circuit elements, not the ideal node assumption.

Therefore the correct choice is c. This matches the provided answer.

Kirchhoff’s Current Law is based on the fact thatSingle choice

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