Series–parallel analysis workflow: when back-solving currents in a series–parallel network, is it good practice to start from the branch farthest from the source and work back toward the source after reducing the network?

Introduction / Context:
Series–parallel circuits are often simplified by successively combining distant sub-networks into equivalent resistances. Once a single equivalent is found and total current is determined, engineers “back-solve” to recover currents and voltages in original branches. This question examines the recommended direction for that back-solving process.

Given Data / Assumptions:

• Passive DC network with clear series and parallel groupings.
• Reduction to an equivalent resistance has already been performed.
• Goal is to determine individual branch currents and drops.
• Ideal source and ohmic elements (no reactive effects).

Concept / Approach:
The canonical method is: reduce the network starting from the portions farthest from the source until you obtain a single equivalent. Then compute total current from the source. Next, expand (reverse the reductions) step by step, starting from the farthest equivalent you formed. At each back-step, apply current-divider and voltage-divider rules as appropriate to recover branch values. This “farthest-outward first” expansion ensures consistency with how the equivalents were formed and avoids mixing knowns with unknowns prematurely.

Step-by-Step Solution:

Verification / Alternative check:
This mirrors standard textbook ladder-network procedures; nodal or mesh analysis would yield identical results but without the intuitive stepwise back-substitution.

Why Other Options Are Wrong:
“Always start at the source” during back-solving can leave critical branch values unknown because later equivalents have not yet been expanded.
“Valid only for AC” or “only if resistors equal” adds constraints that do not apply to the general DC method.

Common Pitfalls:
Confusing reduction order with back-solving order; forgetting to re-apply correct current- or voltage-divider relations when expanding each equivalent stage.

Final Answer:
Valid (standard back-solving sequence)