Inspect
Review the problem, diagram, and evidence.
Both reactive components looked like opposition. At resonance, they canceled and the current doubled the protection 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 rms source drives a series RLC circuit with R = 20 Ξ©, L = 100 mH, and C = 100 Β΅F. The branch is protected for 0.25 A. The technician assumes the inductor and capacitor both add opposition, but near 50.3 Hz the current rises to 0.50 A and protection operates. Find the resonance condition, explain why the reactive terms do not add, and choose a safe correction while keeping the source, L, and C unchanged.
Find the root cause, confirm the fix, and see how this connects to the exam.
Series resonance reduced the impedance to about 20 Ξ©, producing 0.50 A.
Inductive and capacitive reactances have opposite signs and cancel at resonance.
Use Z = R + j(XL - XC); at resonance, |Z| = R and I = V/R.
In a series RLC circuit, impedance is Z = R + j(XL - XC). At resonance XL = XC, so the reactive terms cancel and the impedance magnitude becomes R. With 10 V rms and 20 Ξ©, the resonant current is 0.50 A.
Use Z = R + j(XL - XC). At series resonance XL = XC, the reactive part is zero, |Z| = R, and current reaches its maximum value V/R.
The net reactance becomes zero, the impedance magnitude is minimized to the series resistance, and current reaches its maximum value for a fixed source voltage.
f0 = 1/(2ΟβLC) β 50.33 Hz.
Their magnitudes are equal, but their signs are opposite, so they cancel in the series impedance.
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.