Parallel circuit fundamentals: which statement correctly describes how current distributes in a parallel network of branches connected across the same source?

Introduction / Context:
Parallel circuits provide multiple paths for current. Understanding how current splits among branches is vital for design (sizing resistors, fuses) and for analysis (Kirchhoff current law, equivalent resistance).

Given Data / Assumptions:

• All branches share the same applied voltage.
• Branch resistances can differ.
• Steady-state conditions; components are ideal.

Concept / Approach:
Ohm law at the branch level gives I_k = V / R_k for branch k. Because V is common across branches, currents generally differ in proportion to 1 / R_k. The source current equals the sum of branch currents: I_total = Σ I_k. Therefore, it is correct that current through each branch can be different depending on its resistance (and the applied voltage).

Step-by-Step Solution:
1) Recognize the defining property of parallel networks: equal voltage across each branch.2) Apply Ohm law per branch: I_k = V / R_k.3) Sum currents to get source current: I_total = Σ (V / R_k).4) Conclude that branch currents vary with branch resistances.

Verification / Alternative check:
Measure with ammeters in each branch; readings differ when R values differ, while a voltmeter shows identical voltage across branches, confirming the principle.

Why Other Options Are Wrong:

• The same current everywhere: That is a series-circuit property, not parallel.
• Total current = total voltage * total resistance: Dimensionally incorrect; correct is I = V / R_eq.
• Total current less than the smallest branch current: False; total is the sum, hence ≥ the largest single branch current.
• None of the above: Incorrect because the first statement is true.

Common Pitfalls:
Confusing series and parallel rules is common. Remember: series → same current, parallel → same voltage.

Final Answer:
The amount of current flow through each branch of a parallel circuit can be different, depending on the resistance of each branch part and the amount of voltage applied to it.