Topology insight — in a purely resistive parallel circuit, does the number of current paths equal the number of resistors?

Introduction / Context:Counting current paths helps visualize how current splits and how removing a branch changes overall behavior. This question formalizes the relationship between branches and current paths in a simple parallel network.

Given Data / Assumptions:

• Each resistor forms its own branch directly between the same two nodes.
• No branching within a branch (i.e., no resistor networks nested inside a single branch).

Concept / Approach:In a basic parallel circuit, each distinct resistor connected across the same two nodes provides an independent path for current. Hence, the number of independent current paths equals the number of parallel resistors. This is the reason why adding another parallel resistor increases total conductance and decreases overall resistance: more paths enable more current for a given voltage.

Step-by-Step Solution:

Verification / Alternative check:Draw a node-branch graph: nodes are vertices; each resistor is an edge between the same two vertices; each edge represents one path carrying branch current.

Why Other Options Are Wrong:

• “False” would only be correct if branches shared internal elements or if some resistors were in series inside a branch, which violates the simple “each element is a separate branch” assumption.

Common Pitfalls:Misidentifying series-parallel combinations as pure parallel; always label nodes to see whether every element truly spans the same two nodes.

Final Answer:True