For a series–parallel resistor network, what is the correct method to compute each component's power dissipation?

Introduction / Context:
Power ratings ensure components operate safely without overheating. In mixed series–parallel circuits, currents and voltages differ across components, so a one-size-fits-all shortcut can be dangerous. The only universally correct approach is to use each element's own voltage and current to compute its power.

Given Data / Assumptions:

• Resistors arranged in a general series–parallel network.
• Steady-state DC operation.
• Ohm's law and basic power relations apply.

Concept / Approach:
For any component: P = V * I = I^2 * R = V^2 / R. Which form you use depends on which quantities are known for that specific element. Because series branches share current and parallel branches share voltage, the element's V and I must be determined locally (not assumed from totals) before computing power.

Step-by-Step Solution:
1) Simplify the network as needed to find node voltages and branch currents.2) For each resistor i, determine either Vi or Ii (or both).3) Compute Pi using Pi = Ii^2 * Ri or Pi = Vi^2 / Ri or Pi = Vi * Ii.4) Verify that ΣPi equals the source power (allowing for rounding), ensuring energy conservation.

Verification / Alternative check:
Kirchhoff's laws guarantee that the sum of individual dissipations equals the input power. Cross-checking with Σ(V_branch * I_branch) provides a robust validation of calculations.

Why Other Options Are Wrong:

• Voltage-division percent squared: Only applies to a simple two-resistor series divider under specific conditions; not general.
• Total current squared * R: Valid only for elements that actually carry the total current (pure series). It fails in parallel sections.
• Percent of total power by ratios: Heuristic, not a law; can be grossly inaccurate.

Common Pitfalls:

• Using the same current for all resistors in a mixed network—incorrect for parallel legs.
• Ignoring tolerance and temperature coefficient that slightly alter actual dissipation.

Final Answer:
individual component parameters