Current division insight — in a parallel circuit, the branch having the largest resistance will have which relative current compared with other branches?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Current division governs how source current splits among parallel branches. Since all branches share the same voltage, the branch current depends inversely on its resistance (Ohm’s law). Given Data / Assumptions: Ideal DC conditions, lumped components. Branches are purely resistive for this question. Each branch sees the same node-to-node voltage. Concept / Approach:Ohm’s law: I = V/R. With equal V across branches, higher R implies lower I. Thus, the largest resistance carries the smallest current. Voltage across each branch is equal and equals the source voltage. Step-by-Step Solution: 1) Express branch currents: I1 = V/R1, I2 = V/R2, …2) Compare for Rlargest: Ilargest = V/Rlargest is the smallest magnitude.3) Conclude: the branch with the largest resistance has the least current.4) Total current equals the sum of branch currents per Kirchhoff’s Current Law. Verification / Alternative check:Compute a quick example (V = 12 V; R = 6 kΩ vs 12 kΩ). Currents are 2 mA and 1 mA respectively, confirming the inverse relation. Why Other Options Are Wrong: Most current: occurs for the smallest resistance, not the largest.Least/Most voltage: all branches have the same voltage in parallel.Same current: only if all resistances are equal. Common Pitfalls:Confusing series/parallel attributes; thinking voltage divides in parallel (it does not). Final Answer:Least current

Current division insight — in a parallel circuit, the branch having the largest resistance will have which relative current compared with other branches?

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