Voltage distribution in parallel circuits: What statement best describes the voltage across any branch of a parallel circuit relative to the source?

Introduction / Context:
In a parallel circuit, each branch is connected directly across the source. Recognizing that the same voltage appears across every branch is foundational for calculating branch currents and powers.

Given Data / Assumptions:

• Ideal DC source and wiring.
• Multiple branches connected in parallel to the same two nodes.

Concept / Approach:
The defining property of parallel connection is common voltage. Regardless of branch resistance or conductance, the branch endpoints share the source nodes, so the branch voltage equals the source voltage.

Step-by-Step Reasoning:
Identify the two nodes of the source.Each branch connects between the same two nodes, thus V_branch = V_source.Branch currents then follow I_branch = V_source / R_branch, differing according to resistance.

Verification / Alternative check:
Using nodal analysis with the source set as the reference (or applied) potential, every branch sees the same node-to-node voltage difference.

Why Other Options Are Wrong:
(a) and (b) relate voltage to total current or total resistance, which is a series-circuit viewpoint. (d) describes series voltage division, not parallel circuits.

Common Pitfalls:
Confusing series and parallel behaviors, especially assuming voltage divides among branches in parallel (it does not).

Final Answer:
is equally applied to all branch conductances