Elec Class

learn electricity hands-on
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ISL-oriented exercises electricity problems with answers, on paper or in the lab

Over 200 general electricity problems with step-by-step answers, chapter by chapter: first as calculations, then carried over to the virtual lab. 15 steps · 210 levels · over 200 worked problems

First levelStep 1 · Direct computation of Q1. Quantity of electricity, level 1 of 14
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The 15 steps each step unlocks the next

  1. 1

    1. 1. Quantity of electricity

    14 levelsLesson: Voltage and current

    Q = I·t, coulombs and ampere-hours, simulated time.

    1. 1Direct computation of Q
    2. 2Current from Q and t
    3. 3Duration of flow
    4. 4Average current of a battery
    5. 5Cell autonomy
    6. 6Starter: brief high current
    7. 7Converting ampere-hours to coulombs
    8. 8Milliampere-hours to coulombs
    9. 9Measure then compute Q
    10. 10Reach a quantity of electricity
    11. 11Predict the quantity of electricity
    12. 12Cell autonomy on a lamp
    13. 13Average current from the counter
    14. 14Where to measure the current?
  2. 2

    2. 2. Electrical resistance

    25 levelsLesson: Ohm's law

    Pouillet's law, diameter and cross-section, temperature effect, conductor wire and ohmmeter.

    1. 1Resistance of a conductor
    2. 2Length of a wire
    3. 3Resistivity of a metal
    4. 4Diameter of a wire
    5. 5Resistivity: from SI to industrial unit
    6. 6From diameter to cross-section
    7. 7From cross-section to diameter
    8. 8Hot resistance (0 °C reference)
    9. 9Hot resistance (25 °C reference)
    10. 10Cold resistance
    11. 11Operating temperature
    12. 12Temperature rise of a winding
    13. 13Carbon filament (negative α)
    14. 14Resistance of a wire with the ohmmeter
    15. 15Set a wire to obtain a resistance
    16. 16Which metal? (voltmeter-ammeter method)
    17. 17Which one is copper?
    18. 18Two wires of the same metal
    19. 19Sizing a line
    20. 20Predict the hot resistance
    21. 21Measure the temperature coefficient
    22. 22Resistance thermometer
    23. 23Predict the cold resistance
    24. 24Carbon filament in the lab
    25. 25Heating and current
  3. 3

    3. 3. Ohm's law

    15 levelsLesson: Ohm's law

    U = R·I with the instruments, prefixes, ranges, admissible voltage.

    1. 1Voltage shown by the voltmeter
    2. 2Resistance of a load
    3. 3Current drawn by an oven
    4. 4Insulation resistance (kV, mA)
    5. 5Millivoltmeter across a small resistance
    6. 6Maximum voltage of a potentiometer
    7. 7Voltmeter-ammeter method
    8. 8Get the wanted current
    9. 9Predict the ammeter reading
    10. 10Misconnected instruments
    11. 11Plot U = f(I) of a resistor
    12. 12How far can the voltage go?
    13. 13Insulation test: choose the range
    14. 14From the colour bands to the current
    15. 15Place the voltmeter and the ammeter
  4. 4

    4. 4. Power and efficiency

    25 levelsLesson: Electric power

    P = W/t, P = U·I, hydraulic and lifting chains, wattmeter, energy meter, generator and motor efficiency.

    1. 1Power of a hotplate
    2. 2Energy used by a kettle
    3. 3Running time of an oven
    4. 4Power of a load (U, I)
    5. 5Resistance from the rating plate
    6. 6Useful energy of a motor
    7. 7Waterfall, turbine and generator
    8. 8Required flow of a waterfall
    9. 9Height of a waterfall
    10. 10Efficiency of a generator
    11. 11Power of a crane motor
    12. 12Lifting time
    13. 13Efficiency of a goods lift
    14. 14Load a hoist can lift
    15. 15Pump motor
    16. 16Kilowatt-hours to kilojoules
    17. 17Connect a wattmeter
    18. 18P = U·I, checked with the wattmeter
    19. 19Predict the energy used
    20. 20Stop at the right time
    21. 21Lamp at its rated power
    22. 22Lamp at another voltage
    23. 23Efficiency of a real generator
    24. 24Efficiency of a motor
    25. 25Which one heats up most?
  5. 5

    5. 5. Resistor groups

    33 levelsLesson: Series and parallel circuits

    Series, parallel, mixed, oven settings, line voltage drop, troubleshooting.

    1. 1Equivalent resistance in series
    2. 2Equivalent resistance in parallel
    3. 3Equivalent resistance of a mixed group
    4. 4Series: from partial to total voltage
    5. 5Series: from total to partial voltages
    6. 6Series: current from the total power
    7. 7Series: unknown resistance from a partial power
    8. 8Parallel: current division
    9. 9Parallel: unknown resistance
    10. 10Resistors given by their rating
    11. 11Oven settings: in parallel
    12. 12Oven settings: in series
    13. 13Line voltage drop: source voltage
    14. 14Line voltage drop: admissible resistance
    15. 15Conductor cut into pieces put in parallel
    16. 16n identical resistors
    17. 17Build a series circuit and read a partial voltage
    18. 18Build a parallel circuit and find the total current
    19. 19Equivalent resistance of a network
    20. 20Three identical resistors, one value to reach
    21. 21The missing resistor
    22. 22Current divider
    23. 23Oven setting 1: a single resistor
    24. 24Oven setting 2: two resistors in parallel
    25. 25Oven setting 3: two resistors in series
    26. 26Rank the oven settings
    27. 27Compensate the line voltage drop
    28. 28Cross-section of a garage line
    29. 29Troubleshoot a series circuit
    30. 30Who is in parallel, who carries the most current?
    31. 31Two halves of a wire in parallel
    32. 32Three loads in parallel: Req
    33. 33Find R₁ thanks to the wattmeter
  6. 6

    6. 6. Generators

    10 levelsLesson: EMF and internal resistance

    E = U + r·I, internal resistance, efficiency, no load and under load.

    1. 1EMF of an accumulator cell
    2. 2Current delivered by an accumulator
    3. 3External resistance of an accumulator
    4. 4Internal resistance of an accumulator
    5. 5Ammeter connected straight across a cell
    6. 6Electrical efficiency of a generator
    7. 7Predict the current of a real cell
    8. 8Measure the internal resistance of a cell
    9. 9No load, then under load
    10. 10Load for a given efficiency
  7. 7

    7. 7. Loads

    10 levelsLesson: EMF and internal resistance

    E′, r′, charging accumulator, motor, efficiency.

    1. 1Voltage needed to recharge an accumulator
    2. 2Maximum charging current
    3. 3EMF of a charging accumulator
    4. 4Internal resistance of a charging accumulator
    5. 5Battery of n cells being charged
    6. 6Useful power of a motor
    7. 7Predict the current of a motor
    8. 8Measure the back-EMF of a motor
    9. 9Get the wanted current in a motor
    10. 10Accumulator being charged
  8. 8

    8. 8. Generalised Ohm's law

    7 levelsLesson: EMF and internal resistance

    ΣE = ΣE′ + ΣR·I, opposition, control rheostat.

    1. 1Generalised Ohm's law: missing EMF
    2. 2Two accumulators in opposition
    3. 3Limiting the charging current
    4. 4Rheostat between a generator and a load
    5. 5Two cells, one motor, two resistors
    6. 6Two cells in opposition
    7. 7Set the rheostat of a motor
  9. 9

    9. 9. Loop and junction laws

    4 levelsLesson: Kirchhoff's current and voltage laws

    Two-source circuits solved with Kirchhoff.

    1. 1Two sources, three branches
    2. 2Two-source ladder
    3. 3Which branch carries the most current?
    4. 4Junction law in the lab
  10. 10

    10. 10. The capacitor

    10 levelsLesson: Capacitors and RC circuits

    Series and parallel groups, charge, energy.

    1. 1Capacitors in series
    2. 2Voltage across a series group
    3. 3Two capacitors in series
    4. 4Missing capacitor of a series group
    5. 5Capacitors in parallel
    6. 6Charge of a parallel group
    7. 7Third capacitor of a parallel group
    8. 8Same energy at another voltage
    9. 9Completing a capacitance
    10. 10Adding a discharged capacitor
  11. 11

    11. 11. Electromagnetism

    22 levelsLesson: Magnetism and magnetic force (F = BIL)

    Coil flux density, flux, cut flux, self-induction, Laplace force.

    1. 1Flux density at the centre of a coil
    2. 2Number of turns for a flux density
    3. 3Current for a given flux density
    4. 4Length of a coil
    5. 5Flux of a coil in air
    6. 6Coil diameter for a given flux
    7. 7Flux with an iron core
    8. 8Permeability of a core
    9. 9Turns to spread over a core
    10. 10EMF induced in a flat coil
    11. 11Fluxmeter probe
    12. 12Primary current from the secondary EMF
    13. 13Conductor sweeping the field lines
    14. 14Speed of a bar in a field
    15. 15Flux density cut by a bar
    16. 16Self-induced EMF
    17. 17Admissible switch-off time
    18. 18Current cut in a coil
    19. 19Laplace force
    20. 20Current for a given force
    21. 21Bar on rails and dynamometer
    22. 22Inductance of a coil
  12. 12

    12. 12. Sinusoidal quantities

    9 levelsLesson: Alternating current

    Period, frequency, angular frequency, phase, peak and RMS values, oscilloscope.

    1. 1From period to frequency
    2. 2Angular frequency of a sinusoidal current
    3. 3Phase at a given instant
    4. 4Instantaneous value of a current
    5. 5RMS value read on the oscilloscope
    6. 6Peak current from the energy
    7. 7RMS EMF of an alternator
    8. 8Kettle: amplitude on the oscilloscope
    9. 9Power from the current amplitude
  13. 13

    13. 13. RLC circuits

    16 levelsLesson: RLC circuits and impedance

    Reactances, impedance, series RLC, parallel groups.

    1. 1Resistive wire on AC
    2. 2Heating element on AC
    3. 3Inductance of a pure coil
    4. 4Capacitance of a pure capacitor
    5. 5Current in a pure inductor
    6. 6Angular frequency from an inductor
    7. 7Current in a perfect capacitor
    8. 8Angular frequency from a capacitor
    9. 9Impedance of a series RLC circuit
    10. 10Resistance of a circuit of known impedance
    11. 11Total voltage of a series RLC
    12. 12Coil resistance from cos φ
    13. 13Resistor and pure inductor in parallel
    14. 14Resistor and capacitor in parallel
    15. 15Real coil and capacitor in parallel
    16. 16Pure inductor and capacitor in parallel
  14. 14

    14. 14. AC power

    6 levelsLesson: Power factor and AC power

    S, P, Q, cos φ, installations with several loads.

    1. 1Powers of a coil
    2. 2Two coils in series
    3. 3Three coils in series
    4. 4Heater and motor at a subscriber
    5. 5Lamps, heater and motor
    6. 6Workshop: tubes, motors and heaters
  15. 15

    15. 15. Power-factor correction

    4 levelsLesson: Power factor and AC power

    Correction capacitor, power method.

    1. 1Correction capacitor for a coil
    2. 2Cos φ of a coil in parallel with a resistor
    3. 3Correcting the cos φ of a motor
    4. 4Workshop: capacitor, heater and cos φ

Who is it for?

  • AudienceThe course 526 exercises (chapters 1 to 15), first as calculations then in the lab.
  • Paceover 200 worked problems
  • HelpA hint, then the full working, for every problem.
  • EquipmentA browser is enough; the lab is more comfortable on a large screen.

Frequently asked questions about this path

Are there any prerequisites?

The first steps go over the basics; if you're a complete beginner, start with the Discovery path.

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Steps unlock in order, but all lessons and all problems remain freely available from the lessons.

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Other learning paths

Simulated time00:00:00
Q = I·t-
W = P·t-

Circuit diagram CEI 60617

How does it work?

Each big hole is a circuit node: you push one leg of a component into it. The 4 small holes around it are connected to it: chips and leads plug in there.

  1. Place a component Drag it from the palette: it snaps onto the grid. R rotates it.
  2. Bridge neighbouring holes Pick the jumper chip (or C) and drag on the board: bridged holes become a single node.
  3. Draw a lead For long links and the power supply: from one big hole to another, or to a terminal.
  4. Close the loop The circuit is solved live (Ohm, Kirchhoff) and the diagram follows.

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