Condition for maximum power transfer — statement check: In a linear DC network, maximum power is transferred to the load when the load resistance equals the Thevenin (source) resistance seen from the load terminals. Evaluate this statement.

Introduction / Context:
The maximum power transfer principle is a staple of circuit design, particularly in instrumentation, audio, and communications. The practical question is: what relationship between the source and load ensures that the load receives the greatest possible power for a given source?

Given Data / Assumptions:

• Linear DC or low-frequency network modeled by a Thevenin source (Vth in series with Rth).
• Load is purely resistive with resistance RL.
• No reactive components or frequency-dependent matching in this simplified statement.

Concept / Approach:
For a Thevenin source, power in the load is P = (Vth^2 * RL) / (Rth + RL)^2. Differentiating with respect to RL and setting the derivative to zero yields the optimum at RL = Rth. This result maximizes load power but does not maximize efficiency (which is 50% at the optimum).

Step-by-Step Solution:

Verification / Alternative check:
Choose Vth and Rth, plot P versus RL; the peak appears at RL = Rth. In AC with complex impedances, the generalized condition is ZL = Zth* (complex conjugate).

Why Other Options Are Wrong:
Incorrect: Conflicts with the calculus optimization result.

Applies only at resonance: Resonance is unrelated to the DC resistive case; in AC, conjugate matching is the general rule.

Requires RL = 0: A short circuit yields zero load power (all power dissipates in the source resistance).

Common Pitfalls:
Confusing maximum power transfer with maximum efficiency. Forgetting that in AC networks with reactance, matching is to the complex conjugate of the source impedance.

Final Answer:
Correct