SPM Electrical & Electronics Engineering Studies cheat sheet

Charge Q is measured in coulombs (C); one electron carries about 1.6 × 10⁻¹⁹ C of negative charge.

Current I = Q/t: one ampere equals one coulomb of charge passing a point per second.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance rises with temperature in metals.

Power P = VI = I²R = V²/R; energy consumed is E = Pt, in joules or kilowatt-hours.

Conductors (copper, aluminium) have low resistivity; insulators (PVC, glass, air) have very high resistivity.

A changing magnetic field induces an EMF (Faraday's law); Lenz's law fixes the induced current direction opposing the change.

Capacitance C = Q/V in farads; capacitors store energy E = ½CV² and block steady direct current.

Inductance L in henries: an inductor opposes change in current, storing energy E = ½LI² in its magnetic field.

SI base units: ampere (A), volt (V), ohm (Ω), watt (W), joule (J), coulomb (C), farad (F), henry (H), hertz (Hz).

Common prefixes: k = 10³, M = 10⁶, G = 10⁹, m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹².

Body current thresholds: about 1 mA perception, 10–30 mA muscular tetanus, 50 mA and above can cause ventricular fibrillation.

The let-go threshold is roughly 10–15 mA AC at 50/60 Hz; DC needs higher current to cause the same effect.

IEC 60479 time–current zones classify shock severity; protective devices must clear faults before dangerous durations.

Earth-leakage (RCD/GFCI) devices trip at 10–30 mA residual current and protect people, not cables.

MCBs protect against overload and short circuit; fuses perform the same duty and must be rated for the circuit.

Lock-out/tag-out and proving dead with a tested voltage indicator precede any work on isolated equipment.

Series: R_total = R₁ + R₂ + …; current is common; voltage divides in proportion to resistance.

Parallel: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is common; current divides inversely with resistance.

Kirchhoff's current law: sum of currents into a node equals sum out (charge conservation).

Kirchhoff's voltage law: algebraic sum of voltages around any closed loop is zero (energy conservation).

Thevenin equivalent: any linear two-terminal network is a voltage source V_th in series with R_th.

Norton equivalent: a current source I_N in parallel with R_N; I_N = V_th/R_th and R_N = R_th.

Superposition applies only to linear circuits: analyse one source at a time, then sum the responses.

Maximum power transfer occurs when load resistance equals source (Thevenin) resistance; efficiency then is 50%.

AC impedance Z = R + jX; reactance X_L = 2πfL and X_C = 1/(2πfC); resonance gives X_L = X_C and minimum impedance.

A diode conducts when forward biased above about 0.7 V (silicon) or 0.3 V (germanium); it blocks reverse current.

A Zener diode regulates voltage in reverse breakdown; a series resistor limits the Zener current.

BJT regions: cutoff (no base current), active (amplifier), saturation (switch fully on); β = I_C/I_B.

MOSFETs are voltage-controlled; gate threshold voltage turns the channel on, and gate current is negligible at DC.

Half-wave rectifier: one diode, output ripple frequency equals supply frequency; full-wave gives twice that.

A bridge rectifier uses four diodes and needs no centre-tapped transformer; output ≈ V_peak − 2 diode drops.

An op-amp has very high open-loop gain; negative feedback sets closed-loop gain, e.g. inverting gain = −R_f/R_in.

A 555 timer in astable mode produces a square wave; frequency depends on R₁, R₂ and C.

A transformer changes AC voltage by the turns ratio V₁/V₂ = N₁/N₂; power is approximately constant (ideal).

Transformer losses are copper (I²R) and iron (hysteresis and eddy current); eddy currents are cut by lamination.

A three-phase induction motor's synchronous speed is N_s = 120f/p; slip s = (N_s − N_r)/N_s.

A DC shunt motor has roughly constant speed with load; a series motor has high starting torque and must never run unloaded.

A synchronous generator's frequency is f = pN/120, where N is rotor speed in rev/min and p is pole count.

Transmission at high voltage reduces line current for the same power, cutting I²R losses; transformers step voltage up and down.

Star (Y) connection gives line voltage = √3 × phase voltage; delta gives line current = √3 × phase current.

The national grid uses step-up transformers at generation, high-voltage transmission, then step-down distribution to consumers.

Open-loop control has no feedback; closed-loop control compares output with a setpoint and corrects the error.

PID control combines proportional, integral (removes steady-state error) and derivative (damps overshoot) actions.

Negative feedback improves bandwidth and stability but reduces gain; positive feedback causes oscillation or latching.

Analogue signals vary continuously; digital signals use discrete levels, giving better noise immunity and easy storage.

Sampling must satisfy the Nyquist criterion: sample rate at least twice the highest signal frequency.

Modulation superimposes information on a carrier: AM varies amplitude, FM varies frequency; FM resists amplitude noise better.

A PLC scans inputs, executes its program and updates outputs cyclically; ladder logic is its common programming form.

Sensors (thermistor, LDR, strain gauge) convert physical quantities to electrical signals for control and measurement.

A design brief states the need, constraints and success criteria before any circuit is built.

Tolerance stack-up: total worst-case error equals the sum of individual component tolerances.

Breadboards suit low-voltage prototypes; soldered stripboard or PCB is used for durable, higher-current builds.

A multimeter in series measures current, in parallel measures voltage; measuring voltage across a low resistance loads the circuit.

An oscilloscope shows waveform shape, amplitude, period and phase; probes must be compensated before measurement.

Engineering drawings follow orthographic projection (first- or third-angle) with dimension lines, tolerances and a title block.

Circuit diagrams use standard IEC symbols; a bill of materials lists every component with reference, value and quantity.

Test reports record method, instrument accuracy, raw data, calculated results and sources of error.

Professional codes require competence, honesty, public safety and disclosure of conflicts of interest.

Only sign off work you are competent to verify; misrepresenting qualifications is a disciplinary offence.

Whistleblowing protects the public when an employer's practice endangers safety; report internally first, then to the regulator.

Designers must consider the full product life cycle: raw materials, manufacture, use, disposal and recycling.

RoHS restricts hazardous substances (lead, mercury, cadmium, certain flame retardants) in electrical products.

WEEE directs waste electrical and electronic equipment to separate collection and recovery, not landfill.

Energy efficiency reduces carbon emissions; renewable generation (wind, solar, hydro) displaces fossil-fuel plant.

Electromagnetic compatibility requires equipment neither to emit excessive interference nor to be upset by it.

Continuity testing uses a low-resistance ohmmeter range with the circuit de-energised and isolated.

Insulation resistance is measured with a high-voltage tester (typically 500 V DC); acceptable values are in megohms.

A short circuit shows near-zero resistance; an open circuit shows infinite resistance on an ohmmeter.

Voltage-drop testing locates high-resistance joints under load better than a static resistance measurement.

Instrument burden affects readings: a voltmeter should have high input impedance, an ammeter very low resistance.

A current clamp measures current without breaking the circuit, using the magnetic field around the conductor.

Thermal imaging reveals overheating connections and overloaded components before failure.

Repeat measurements and compare with expected values; a single reading without context is not diagnostic evidence.