Parallel RL networks: which statement correctly describes the voltage across the resistor and the inductor in a parallel R–L circuit?

Introduction / Context:
In parallel circuits, all elements share the same two nodes. This fundamental topology rule implies that the node-to-node voltage is identical across each branch, independent of the branch impedance or current.

Given Data / Assumptions:

• An ideal resistor and ideal inductor connected in parallel across an AC source.
• Sinusoidal steady state; no coupling effects.
• We refer to branch voltages (across R and across L).

Concept / Approach:
By definition of parallel connection, the branch voltages are identical in amplitude and phase because both ends of each component connect to the same pair of nodes. What differs are the branch currents: resistive current is in phase with the voltage; inductive current lags by 90 degrees in an ideal inductor. The total supply voltage is simply the common node voltage, not a sum of branch voltages.

Step-by-Step Solution:
Identify topology: R and L in parallel share the same node voltage.State rule: V_R = V_L = V_source (same amplitude and phase).Conclude: option (a) is correct since voltage is the same across each branch.

Verification / Alternative check:
KCL writes I_total = I_R + I_L; KVL around any loop including the source and a branch enforces the same node voltage across each branch element.

Why Other Options Are Wrong:
Sum of voltages: applies to series elements, not parallel branches.Total voltage lag relationship: phase relation is between total current and voltage, not a statement about branch voltages.“Less than the sum”: still misapplies series thinking to a parallel circuit.

Common Pitfalls:
Confusing series with parallel rules; conflating current phasors (which differ by branch) with voltage (which is common to all branches).

Final Answer:
The voltage always has the same amplitude and phase for every part of the circuit