First objective in series–parallel analysis: When approaching a complex series–parallel circuit, what should be the first goal to accomplish in order to simplify subsequent steps?

Introduction / Context:
Effective analysis of mixed series–parallel networks follows a logical sequence. Establishing the global behavior first makes local calculations straightforward and reduces the chance of arithmetic or conceptual errors. This question asks for the appropriate first objective.

Given Data / Assumptions:

• Circuit contains a combination of series and parallel elements.
• Source values are known.
• Goal is to find currents and voltages throughout the network.

Concept / Approach:
The most efficient starting point is to reduce the network to an equivalent total resistance and use it with the known source to determine total current. With total current and the high-level equivalent known, you can progressively “expand” the circuit back out, computing intermediate node voltages and branch currents via divider rules and parallel current splits. Jumping directly to every voltage drop without a global reference invites mistakes.

Step-by-Step Solution:
Combine obvious series or parallel groups into a single equivalent resistance step by step.Compute the overall equivalent resistance R_eq as seen by the source.Use Ohm’s law to find the total current: I_total = V_source / R_eq.Back-substitute: from the source toward the loads, split currents at parallel nodes and apply voltage division across series parts to find individual drops.

Verification / Alternative check:
Perform a quick power balance: P_source = V_source * I_total should equal the sum of I^2 * R losses in all elements after detailed calculations. Matching totals confirms consistency.

Why Other Options Are Wrong:
Equate all parallel or series components: you cannot equate dissimilar values; you reduce them to equivalents, but that is part of building R_eq, not an end in itself.Solve for all voltage drops: without I_total and key node voltages, this is premature and error-prone.

Common Pitfalls:
Ignoring unit conversions (Ω, kΩ) and rounding too early. Another pitfall is forgetting that total current is unique to the source loop but branches split according to conductances in parallel sections.

Final Answer:
solve for the total current and resistance