Norton to Thevenin conversion: A current source has IS = 4 µA in parallel with RS = 1.2 MΩ. Determine the equivalent Thevenin source (VTH and RTH).

Introduction / Context:Converting between Norton and Thevenin equivalents is a standard analysis tool for simplifying linear circuits. A Norton current source in parallel with a resistance can be replaced by a Thevenin voltage source in series with the same resistance, keeping terminal behavior unchanged.

Given Data / Assumptions:

• Norton current IS = 4 µA.
• Norton resistance RS (parallel) = 1.2 MΩ.
• Linear, time-invariant network, steady state.

Concept / Approach:

The relationships are VTH = IS * RS and RTH = RS. The resistance value is preserved across the transformation, while the source form changes from current to voltage.

Step-by-Step Solution:

Verification / Alternative check:

Open-circuit voltage of the Norton form is IS * RS = 4.8 V, matching VTH. Short-circuit current of the Thevenin form is VTH / RTH = 4.8 V / 1.2 MΩ = 4 µA, matching IS. Equivalence confirmed.

Why Other Options Are Wrong:

4.8 µV is six orders too small. 1 V is not IS * RS. 4.8 V, 4.8 MΩ incorrectly changes resistance. 0.48 V, 120 kΩ also changes both values without basis.

Common Pitfalls:

Unit slips (µA and MΩ), and forgetting that RTH equals RS exactly in this transformation.

Final Answer:

4.8 V, 1.2 MΩ