Series network power accounting: Four series resistors dissipate 16 mW, 107 mW, 146 mW, and 243 mW respectively. What is the total power consumed by the entire circuit?

Introduction:
In any series circuit, the total power drawn from the source equals the sum of the powers dissipated in each element. This conservation-based reasoning is essential for thermal design, resistor wattage selection, and overall efficiency analysis.

Given Data / Assumptions:

• P1 = 16 mW, P2 = 107 mW, P3 = 146 mW, P4 = 243 mW.
• Resistors are in series and all listed power values are steady-state.
• No additional significant losses elsewhere (e.g., wiring losses negligible).

Concept / Approach:

Total power in a series circuit is additive: P_total = Σ P_i. This follows from energy conservation and from P = V * I with the series current common to all branches; individual voltage drops differ, but energy sums linearly.

Step-by-Step Solution:

Verification / Alternative check:

If the source voltage and series current were known, P_total could also be confirmed using P_total = V_source * I_series, which would equal the sum of resistor powers by conservation of energy, reinforcing the result 512 mW.

Why Other Options Are Wrong:

• 128 mW / 269 mW / 396 mW: Intermediate or incorrect partial sums.
• 1024 mW: Double the correct value; no basis in the provided numbers.

Common Pitfalls:

• Mistaking average or RMS values; the question already provides dissipations, which add directly.
• Confusing power summation with resistance addition; both are linear in series circuits, but they represent different physical quantities.

Final Answer:

512 mW