Inspect
Review the problem, diagram, and evidence.
The divider measured exactly 6 V with no load. Connect one load, and the output falls to 4 V.
Inspect, commit, prove, fix, and sign off.
Follow the investigation process used in the field — in five guided steps.
Review the problem, diagram, and evidence.
Choose your hypothesis.
Run calculations and test your idea.
Select and validate a safe correction.
See the full debrief and key takeaways.
A 12 V source feeds a divider made from a 10 kΩ top resistor and a 10 kΩ lower resistor. The midpoint measures 6 V with no load. A 10 kΩ load is then connected from the midpoint to ground, and the output falls to 4 V. Diagnose why the unloaded calculation no longer applies and choose a correction that restores 6 V for this known load.
Find the root cause, confirm the fix, and see how this connects to the exam.
The 10 kΩ load paralleled the 10 kΩ lower resistor, reducing the effective lower leg to 5 kΩ.
The unloaded divider formula was applied after the load changed the network.
Reduce the actual loaded network first, then calculate Vout from the resulting divider ratio.
A finite load changes a voltage divider because it becomes part of the lower leg. Here, a 10 kΩ load in parallel with the 10 kΩ lower resistor gives 5 kΩ, so Vout = 12 × 5/(10+5) = 4 V instead of 6 V.
Before applying the voltage-divider equation, include the connected load in the circuit model. Reduce the loaded lower leg to its equivalent resistance, then calculate the divider output.
A load connected from the output to ground is in parallel with the lower divider resistor. That reduces the effective lower resistance and changes the divider ratio.
The equivalent resistance is 5 kΩ.
First combine the load with the resistor it parallels, then use that equivalent resistance in the voltage-divider equation.
Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — and beyond.
Basic subject familiarity helps, but every case is designed to teach through the investigation itself.
Most cases are designed for a focused 5–10 minute investigation.
Each case is mapped to a verified exam, subject, topic, and misconception before publication.
The sealed debrief unlocks with the root cause, corrected reasoning, fix, and takeaway.