Thevenin’s theorem application: when simplifying a linear two-terminal network seen by a load, what is the standard Thevenin equivalent?

Introduction / Context:
Thevenin’s theorem is a cornerstone of circuit simplification. It allows any linear, bilateral network to be replaced at a pair of terminals by an equivalent source and resistance, making load analysis straightforward, especially during design and troubleshooting.

Given Data / Assumptions:

• Network is linear and time-invariant over the operating range.
• Independent/dependent sources and resistors may be present.
• We seek the two-terminal equivalent as seen by a load.

Concept / Approach:
The Thevenin equivalent comprises an ideal voltage source V_th in series with a resistance R_th. To determine V_th, compute the open-circuit voltage at the terminals. To determine R_th, zero all independent sources (voltage sources → short, current sources → open) and find the equivalent resistance seen into the network (or use the short-circuit current method: R_th = V_th / I_sc).

Step-by-Step Solution:
Remove the load and compute V_th (open-circuit terminal voltage).Suppress independent sources and calculate R_th from the terminals.Build the Thevenin model: V_th in series with R_th feeding the load.

Verification / Alternative check:
Norton’s theorem is the dual: an ideal current source I_n in parallel with R_n. The two forms are interchangeable via source transformation where V_th = I_n * R_n and R_th = R_n.

Why Other Options Are Wrong:
Current source with parallel resistor: that describes Norton, not Thevenin.Voltage source with parallel resistor or current source with series resistor: not standard equivalents for a general two-terminal linear network.None of the above: incorrect since the standard form is listed.

Common Pitfalls:
Confusing Thevenin with Norton; forgetting to deactivate dependent sources properly (they remain, controlled by their variables); mixing open-circuit and short-circuit methods.

Final Answer:
Ideal voltage source and series resistor