Current distribution in parallel circuits: Does the branch with the lowest resistance carry the greatest current when branches share the same voltage?

Introduction / Context:
Parallel circuits place components across the same two nodes, so each branch experiences the same voltage. This item checks the fundamental current-voltage-resistance relationship governing how current divides among parallel branches.

Given Data / Assumptions:

• Ideal voltage source maintains node-to-node voltage across all branches.
• Branches contain resistors (linear, time-invariant).
• Steady-state DC or AC using RMS values for magnitudes.

Concept / Approach:

Ohm’s law states I = V / R. In a parallel network, each branch current Ik equals V / Rk. If two branches share the same V, the smaller Rk produces a larger Ik. Thus, the branch with the lowest resistance draws the most current.

Step-by-Step Solution:

Verification / Alternative check:

Numerical example: V = 12 V; R1 = 3 Ω, R2 = 6 Ω. I1 = 4 A, I2 = 2 A. The lower resistance branch indeed carries twice the current.

Why Other Options Are Wrong:

• No need for other branches to be open; current division works with any number of branches.
• In AC, the same principle holds for resistive branches using RMS values.
• Power rating does not determine current; resistance and voltage do.

Common Pitfalls:

Confusing resistance with power rating or physical size. Also, treating parallel branches as if currents must be equal—this only occurs when the resistances are equal.

Final Answer:

True