Current division in parallel circuits — does total current split directly proportional to resistance values?

Introduction / Context:Understanding how current divides among parallel branches is essential for sizing components and predicting power dissipation. This item targets the proportionality rule for current division.

Given Data / Assumptions:

• Two or more resistors connected in parallel across a common voltage source.
• Ohmic behavior (linear resistors) and steady-state conditions.

Concept / Approach:In parallel, branch voltages are equal. Using Ohm’s law, branch current Ik = V / Rk. Therefore, current in a branch is inversely proportional to its resistance. Lower resistance draws more current, higher resistance draws less. The current divider formula for two branches is I1 = Itot * (R2 / (R1 + R2)), I2 = Itot * (R1 / (R1 + R2)). Note that each branch current multiplies by the opposite branch resistance in the numerator, embodying inverse proportionality.

Step-by-Step Solution:

Verification / Alternative check:Example: V = 10 V, R1 = 5 Ω, R2 = 10 Ω → I1 = 2 A, I2 = 1 A. The branch with half the resistance draws twice the current, consistent with inverse proportionality.

Why Other Options Are Wrong:

• “True” would claim larger resistors get more current, which contradicts Ohm’s law under equal voltage.

Common Pitfalls:Memorizing formulas without noting symmetry: the “opposite resistance” in the numerator is a cue that current is inversely related to resistance.

Final Answer:False