In AC circuit analysis using Thevenin’s theorem, the reduced Thevenin equivalent seen by a load consists of which two components? Select the most accurate pair for sinusoidal steady-state (phasor) conditions.

Introduction / Context:
Thevenin’s theorem is a cornerstone of network reduction in electrical engineering. For any linear, bilateral network seen from two terminals, we can compute an equivalent that behaves identically at those terminals. In alternating current (AC) phasor analysis, this equivalent is expressed with complex quantities to capture both resistance and reactance, allowing us to predict current, voltage, and power for any attached load quickly.

Given Data / Assumptions:

• We are working under sinusoidal steady-state, so impedances (not just resistances) represent elements.
• The original network is linear and bilateral.
• We want the correct composition of the Thevenin equivalent as seen by a load.

Concept / Approach:
The Thevenin equivalent across two terminals is formed by: (1) the open-circuit (no-load) voltage at those terminals, called V_TH, and (2) an equivalent series impedance Z_TH that accounts for the network’s internal opposition to current (including resistive and reactive parts). Z_TH is found by deactivating independent sources (voltage sources shorted, current sources opened) and calculating the equivalent impedance seen into the network.

Step-by-Step Solution:

Verification / Alternative check:
Replace the reduced model with an arbitrary load Z_L. Compute I = V_TH / (Z_TH + Z_L). If you instead analyze the original network directly, you obtain the same terminal current and load voltage. This identity validates that the pair {V_TH, Z_TH in series} completely characterizes terminal behavior.

Why Other Options Are Wrong:

• 'the equivalent voltage source and the equivalent series resistance': In AC phasor form, opposition is complex; using only resistance ignores reactance, so this is incomplete.
• 'the equivalent voltage source and the equivalent parallel impedance': Thevenin uses a series element; a parallel form corresponds to Norton after source conversion.
• 'the equivalent voltage source and the equivalent parallel resistance': Again, parallel form is a Norton construct and resistance alone is insufficient in AC.

Common Pitfalls:

• Confusing Thevenin (series source + series impedance) with Norton (current source + parallel admittance/impedance) forms.
• Forgetting to deactivate sources correctly when computing Z_TH (short ideal voltage sources, open ideal current sources).

Final Answer:
the equivalent voltage source and the equivalent series impedance