Electrical engineering basics: 50 core concepts

All 50 cards

1. 1
   Electric charge: symbol and unit
   $Q$, measured in coulombs (C)

   An electron carries $-1.602 \times 10^{-19}\ \mathrm{C}$, so one coulomb is about $6.24 \times 10^{18}$ electrons.
2. 2
   Electric current
   The rate of flow of charge: $I = \dfrac{Q}{t}$, measured in amperes (A)

   $1\ \mathrm{A} = 1\ \mathrm{C/s}$
3. 3
   Voltage (potential difference)
   The work done per unit charge in moving charge between two points: $V = \dfrac{W}{Q}$, measured in volts (V)

   $1\ \mathrm{V} = 1\ \mathrm{J/C}$
4. 4
   Resistance
   Opposition to current: $R = \dfrac{V}{I}$, measured in ohms ($\Omega$)

   Its reciprocal is conductance, $G = 1/R$, measured in siemens (S).
5. 5
   Conventional current vs electron flow
   Conventional current flows from positive to negative through the external circuit; electrons drift the opposite way

   Circuit diagrams and the arrows in component symbols use conventional current.
6. 6
   SI prefixes k, M and G
   Kilo $10^3$, mega $10^6$, giga $10^9$

   Capital M is mega and lowercase m is milli: $4.7\ \mathrm{M\Omega} = 4\,700\,000\ \Omega$.
7. 7
   SI prefixes m, µ, n and p
   Milli $10^{-3}$, micro $10^{-6}$, nano $10^{-9}$, pico $10^{-12}$

   Example: $100\ \mathrm{nF} = 0.1\ \mathrm{\mu F} = 100\,000\ \mathrm{pF}$.
8. 8
   Kilowatt-hour (kWh)
   The energy used by $1\ \mathrm{kW}$ for one hour: $3.6\ \mathrm{MJ}$

   Energy is power times time, $E = Pt$: a $2\ \mathrm{kW}$ heater running for 3 hours uses $6\ \mathrm{kWh}$.
9. 9
   Ohm’s law
   $V = IR$

   It holds for ohmic conductors such as resistors at a constant temperature. Diodes and filament lamps are non-ohmic.
10. 10
    Electric power
    $P = VI = I^2R = \dfrac{V^2}{R}$

    Measured in watts: $1\ \mathrm{W} = 1\ \mathrm{J/s}$.
11. 11
    Kirchhoff’s current law (KCL)
    The total current flowing into a node equals the total current flowing out

    It follows from conservation of charge.
12. 12
    Kirchhoff’s voltage law (KVL)
    The voltages around any closed loop sum to zero

    It follows from conservation of energy.
13. 13
    Resistance of a wire
    $R = \dfrac{\rho L}{A}$

    $\rho$ is the resistivity, $L$ the length and $A$ the cross-sectional area. Copper’s resistivity is about $1.7 \times 10^{-8}\ \Omega\,\mathrm{m}$ at 20 °C.
14. 14
    Terminal voltage of a battery
    $V = \mathcal{E} - Ir$

    $\mathcal{E}$ is the EMF and $r$ the internal resistance, so the voltage sags as the current $I$ rises.
15. 15
    Resistors in series
    $R_{\text{eq}} = R_1 + R_2 + \cdots$

    The same current flows through each one, and their voltages add up.
16. 16
    Resistors in parallel
    $\dfrac{1}{R_{\text{eq}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$

    Each has the same voltage across it, and the total is less than the smallest resistance.
17. 17
    Two resistors in parallel (shortcut)
    $R_{\text{eq}} = \dfrac{R_1 R_2}{R_1 + R_2}$

    Product over sum. Two equal resistors give half the value: $10\ \mathrm{k\Omega} \parallel 10\ \mathrm{k\Omega} = 5\ \mathrm{k\Omega}$.
18. 18
    Voltage divider
    $V_{\text{out}} = V_{\text{in}}\,\dfrac{R_2}{R_1 + R_2}$

    $V_{\text{out}}$ is taken across $R_2$. It holds only while the load draws negligible current.
19. 19
    Current divider (two resistors)
    $I_1 = I\,\dfrac{R_2}{R_1 + R_2}$

    The larger share of the current flows through the smaller resistance.
20. 20
    Resistor colour code: digits 0 to 9
    Black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9

    The colours from red to violet follow the order of the rainbow.
21. 21
    Resistor tolerance bands: gold and silver
    Gold ±5%, silver ±10%

    Precision resistors use brown (±1%) or red (±2%).
22. 22
    Value of a resistor banded brown, black, red, gold
    $1\ \mathrm{k\Omega}$ ±5%

    Brown 1 and black 0 give 10, and the red multiplier band means $\times 10^2$: $10 \times 100 = 1000\ \Omega$.
23. 23
    Ceramic capacitor marked 104
    $100\ \mathrm{nF}$ ($0.1\ \mathrm{\mu F}$)

    The first two digits are the value and the third is the number of zeros, in picofarads: $10 \times 10^4\ \mathrm{pF}$.
24. 24
    Capacitance
    $C = \dfrac{Q}{V}$, measured in farads (F)

    A capacitor stores energy in the electric field between two conductors separated by an insulator.
25. 25
    Energy stored in a capacitor
    $E = \tfrac{1}{2}CV^2$
26. 26
    Capacitors in series and in parallel
    Parallel: $C_{\text{eq}} = C_1 + C_2 + \cdots$. Series: $\dfrac{1}{C_{\text{eq}}} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \cdots$

    The opposite of the rules for resistors.
27. 27
    Current through a capacitor
    $i = C\,\dfrac{dv}{dt}$

    A capacitor passes current only while the voltage across it is changing.
28. 28
    Voltage across an inductor
    $v = L\,\dfrac{di}{dt}$

    Inductance is measured in henries (H). An inductor stores energy in its magnetic field.
29. 29
    Energy stored in an inductor
    $E = \tfrac{1}{2}LI^2$
30. 30
    Capacitors and inductors in a DC circuit at steady state
    A capacitor acts as an open circuit; an inductor acts as a short circuit

    Nothing is changing, so no current flows into the capacitor and no voltage appears across the inductor.
31. 31
    Electrolytic capacitors
    They are polarized: the lead marked negative must be at the lower voltage

    Connected in reverse or over their rated voltage, they can overheat, vent or burst.
32. 32
    AC vs DC
    Direct current flows in one direction only; alternating current reverses direction periodically, usually as a sine wave

    Batteries supply DC; the mains supply is AC.
33. 33
    Frequency and period
    $f = \dfrac{1}{T}$

    Frequency is measured in hertz (cycles per second): a $50\ \mathrm{Hz}$ wave has a period of $20\ \mathrm{ms}$.
34. 34
    Mains frequency
    $50\ \mathrm{Hz}$ in most of the world; $60\ \mathrm{Hz}$ in North America and some other countries

    Japan uses both: 50 Hz in the east and 60 Hz in the west.
35. 35
    RMS value of a sine wave
    $V_{\text{rms}} = \dfrac{V_{\text{peak}}}{\sqrt{2}} \approx 0.707\,V_{\text{peak}}$

    The RMS value is the DC voltage that would heat a resistor at the same average rate.
36. 36
    Peak voltage of 230 V mains
    About $325\ \mathrm{V}$ ($230\sqrt{2}$)

    Mains voltages are quoted as RMS values. For 120 V mains the peak is about 170 V.
37. 37
    Diode
    Lets current flow from anode to cathode and blocks it in the reverse direction

    In the symbol the arrow points the way conventional current flows, and the bar marks the cathode.
38. 38
    Forward voltage of a silicon diode
    About $0.6$ to $0.7\ \mathrm{V}$

    Schottky diodes drop less, typically about 0.2 to 0.4 V.
39. 39
    Series resistor for an LED
    $R = \dfrac{V_s - V_F}{I_F}$

    $V_s$ is the supply, $V_F$ the LED’s forward voltage (about $2\ \mathrm{V}$ for red, $3\ \mathrm{V}$ for blue or white) and $I_F$ the current, often $10$ to $20\ \mathrm{mA}$.
40. 40
    Terminals of a BJT and a MOSFET
    BJT: base, collector, emitter. MOSFET: gate, drain, source

    The base and the gate are the control terminals.
41. 41
    Transistor used as a switch
    A small signal at the base or gate turns a much larger current between the other two terminals fully on or fully off

    A BJT is driven by base current; a MOSFET by gate voltage, with almost no steady gate current.
42. 42
    Relay
    An electrically operated switch: current through a coil moves a set of contacts

    It lets a small circuit control a separate, isolated circuit at a higher voltage or current.
43. 43
    Flyback diode across a relay coil
    It gives the coil’s current a path when the coil is switched off, preventing a voltage spike that could destroy the driving transistor

    It is fitted reverse-biased, so it carries no current while the coil is energized.
44. 44
    Fuse
    A thin conductor that melts and breaks the circuit when the current exceeds its rating

    It protects the wiring from overheating. A circuit breaker does the same job and can be reset.
45. 45
    How to connect an ammeter and a voltmeter
    An ammeter goes in series with the component; a voltmeter goes in parallel across it

    An ideal ammeter has zero resistance and an ideal voltmeter infinite resistance, so neither disturbs the circuit.
46. 46
    Short circuit vs open circuit
    A short circuit is a path of almost zero resistance (no voltage across it); an open circuit is a break (no current through it)
47. 47
    Ground in a circuit diagram
    The reference node, defined as 0 V, that other node voltages are measured from

    It need not be connected to the earth; protective earth is a separate safety connection.
48. 48
    Protective earth
    A conductor connecting exposed metal parts of equipment to earth, so a fault makes a large current flow and blows the fuse or trips the breaker instead of leaving the case live
49. 49
    Residual-current device (RCD or GFCI)
    Cuts the supply when the currents in the live and neutral conductors differ, meaning current is leaking to earth, possibly through a person

    Typical trip thresholds are 30 mA for an RCD and about 5 mA for a GFCI.
50. 50
    Mains wire colours (IEC)
    Brown: live. Blue: neutral. Green and yellow: protective earth

    In North America, black (or red) is hot, white is neutral and green or bare copper is ground.