Prerequisites
DC circuit laws, voltage division, parallel resistance and differentiation of rational functions.
An ideal 6 V source feeds R_top = 1000 ohms and R_bottom = 1000 ohms in series. The output port is across R_bottom. V_th is the unloaded port voltage. To find R_th in this drawing, replace the independent ideal voltage source with a wire, giving R_top parallel R_bottom. This is a paper transformation, never a physical short. Use diagrams and calculations only. Never use wall outlets, short batteries, open powered equipment or handle charged capacitors.
Worked example
The port equivalent is V_th = 3 V in series with R_th = 500 ohms. With a 1000-ohm load, I_load = 3/(500 + 1000) = 0.002 A and V_load = 2 V.
Further inquiry
Derive the port voltage and equivalent resistance from the original divider, then express load power as a function of positive load resistance. Differentiate to locate the maximum and compare power-transfer efficiency there with the light-load limit. Explain why a mathematical source-deactivation step is not an instruction to short a real source.
Review criteria
- State the source, component, initial-state and load assumptions explicitly.
- Show units, intermediate derivations and limiting-case checks.
- Separate a mathematical circuit transformation from any physical equipment procedure.