Inspect
Review the problem, diagram, and evidence.
The steady-state current is zero. At switch-on, the circuit violates its 5 mA startup limit.
Inspect, commit, prove, fix, and sign off.
Follow the investigation process used in the field β 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 10 V DC source is connected through a 1 kΞ© resistor to an initially uncharged 1000 Β΅F capacitor. The design review says the capacitor is an open circuit on DC, so the branch current should be zero. In testing, the startup current reaches 10 mA, exceeding a 5 mA design requirement. Diagnose the missing initial-condition check, calculate the time constant, and choose a resistor that satisfies the startup-current limit.
Find the root cause, confirm the fix, and see how this connects to the exam.
The initially uncharged capacitor made the 1 kΞ© resistor carry 10 mA at t = 0+.
The open-circuit capacitor rule is a DC steady-state result, not the switching-instant model.
Use capacitor-voltage continuity first, then calculate i(0+) and the RC time constant.
An initially uncharged capacitor has 0 V across it at t = 0+, so a series resistor initially sees the full source voltage. With 10 V and 1 kΞ©, the initial current is 10 mA; it then decays exponentially with time constant RC.
Use the capacitor's initial voltage at t = 0+ before applying the steady-state model. For an initially uncharged RC circuit, i(0+) = V/R and the current then decays exponentially with time constant RC.
Its voltage cannot change instantaneously, so it begins at its initial voltage and the series resistor initially carries current set by the source voltage and resistance.
i(0+) = 10 V / 1 kΞ© = 10 mA.
Ο = RC = 1 second.
Each case is designed to build the judgment, analysis, and confidence you need for engineering exams β and beyond.
Basic subject familiarity helps, but every case is designed to teach through the investigation itself.
Most cases are designed for a focused 5β10 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.