Topology identification rule: Which fundamental aspect determines whether interconnected resistors form a series, parallel, or series–parallel circuit in DC analysis?

Introduction / Context:
Recognizing circuit topology quickly is essential for applying the correct solving technique. The essence of “series” and “parallel” lies in how current can flow: one path or multiple paths. This conceptual clarity avoids mistakes when redrawing or simplifying networks.

Given Data / Assumptions:

• Standard DC circuits with ideal wires and components.
• Definitions: series = one current path; parallel = multiple current paths between the same two nodes.
• No reactive effects considered.

Concept / Approach:
The classification hinges on current paths. If there is only one path for current through components sequentially, they are in series. If components share both terminal nodes (same two nodes), they are in parallel, providing multiple current paths. Mixed combinations create series–parallel networks.

Step-by-Step Solution:

Verification / Alternative check:
Redraw the circuit using node labeling. Components that bridge the same node pair are parallel; elements chained between successive nodes are in series. This method consistently matches the “current paths” criterion.

Why Other Options Are Wrong:
Source type, “voltage flow,” wattage rating, or physical spacing do not define topology. Only connection nodes and consequent current paths do.

Common Pitfalls:
Letting physical drawing layout (left/right, up/down) mislead you; rely on node connections, not artwork.

Final Answer:
Current flow (number of available paths)