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Foundation module

Electrical Circuits and Sensors

Learn voltage, current, resistance, power, sensor signals, calibration, filtering, and actuator interfaces.

Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.

01

Readiness check

Before starting, confirm the prerequisite habits.

  • Use Ohm law.
  • Read simple series circuits.
  • Know voltage is measured across elements.
  • Understand sensor calibration conceptually.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02

The core idea

Build and interpret simple circuits that measure mechanical quantities.

Circuit analysis rests on two laws (KCL at nodes and KVL around loops) and most sensor interfaces reduce to a voltage divider whose output you can predict before touching a meter.

Vout = Vin R2/(R1+R2)
Works when: you reduce the network with KCL/KVL or a divider and predict the node voltage before measuring.
Breaks down when: you treat a loaded divider as unloaded, ignoring the current the next stage draws.
Figure 1. Concept model for Electrical Circuits and Sensors. The figure names inputs, computed variables, geometry, and result.
input/load result/constraint computed variable dimension/model geometry
03

The method

1Model

Make the physical situation visible.

2Relate

Translate the model into symbols.

3Solve

Calculate only after the model is clear.

4Check

Use units, scale, and limiting cases.

04

Worked example

Figure 2. Worked problem setup: A 10 k ohm resistor is in series with a 5 k ohm sensor resistor across 5 V. Vout is measured across the 5 k ohm resistor. Find Vou
Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.

A 10 k ohm resistor is in series with a 5 k ohm sensor resistor across 5 V. Vout is measured across the 5 k ohm resistor. Find Vout.

  1. Problem A 10 k ohm resistor is in series with a 5 k ohm sensor resistor across 5 V. Vout is measured across the 5 k ohm resistor. Find Vout.
  2. Given and find Vin = 5 V, R1 = 10 k ohm, R2 = 5 k ohm. Find: Vout across R2.
  3. Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
  4. Step Use the voltage divider equation.
  5. Step Vout = 5(5)/(10+5) = 1.67 V.
  6. Step Output is one third of supply because R2 is one third of total resistance.
  7. Step Confirm the measuring device has high input impedance.
  8. Conclusion Vout = 1.67 V. Carry this result into the design decision, not just into the answer box.
05

Misconceptions and diagnostics

MistakeSymptomDiagnostic questionCorrection
Ignoring loadingDivider output sags under loadDoes the next stage draw current?Account for load resistance in parallel.
Series vs. parallel mix-upAdds resistances that are in parallelSame current or same voltage across them?Series share current; parallel share voltage.
Units and prefixesk ohm and mA mismatchedAre your units consistent (V, A, ohm)?Convert prefixes before computing.
06

Practice ladder

Level 1: direct skill

Redo the worked example with one changed input. Predict the trend before calculating.

Check yourself

The trend must match the governing relation: Vout = Vin R2/(R1+R2).

Level 2: mixed concept

Draw the model from memory, label knowns and unknowns, then write the first equation without looking.

Check yourself

Your first equation should connect the model to Vout.

Level 3: independent problem

Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.

Check yourself

A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.

Level 4: transfer task

Turn the result into a design decision: what would you change if the output missed its target by 25 percent?

Check yourself

Name the design variable with the strongest influence and justify it from the equation.

07

Working with AI, and proving it yourself

Useful AI role

Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.

Do not outsource

Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.

08

Retrieval and spaced review

Closed-notes prompts: draw the circuit, apply KCL at a node or KVL around a loop, write the divider output, and state how a load would change it.

TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09

Mapping and portfolio task

Course mapping

Circuits and sensors are the front end of mechatronics and controls: the divider and op-amp reasoning here is how every measured signal reaches your controller.

First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.

Portfolio task

Create a one-page sensor-interface note (divider design and loading check): sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.