Current divider principle: evaluate the statement that the most current flows in the parallel path which has the greatest resistance value.

Introduction / Context:
The current divider rule is a cornerstone of basic circuit analysis. It predicts how a total current distributes between or among parallel impedances. The tested claim is the exact opposite of what the rule states, making this a good quick check of conceptual accuracy in DC resistive networks.

Given Data / Assumptions:

• Parallel resistive branches excited by a source with fixed voltage.
• Linear time-invariant components.
• No reactive effects considered for this DC statement.

Concept / Approach:
For two branches R1 and R2, the current through R1 is I_total * (R2 / (R1 + R2)). This shows that as R1 increases, I_through_R1 decreases, because the numerator contains the other branch resistance. Extending to multiple branches, the path with the smallest resistance draws the largest share of current. Therefore, the statement claiming the most current in the greatest resistance path is incorrect.

Step-by-Step Solution:

Verification / Alternative check:
Check with simple numbers: with V = 10 V, R_small = 1 ohm gives 10 A, R_large = 10 ohm gives 1 A. The smaller resistance indeed carries more current.

Why Other Options Are Wrong:
Correct: contradicts the divider rule.
High frequency or inductive qualifiers do not reverse the inverse law for purely resistive DC networks.

Common Pitfalls:
Confusing series rules with parallel rules; misapplying proportional reasoning.

Final Answer:
Incorrect