Module 3 Electrical Fundamentals cheat sheet

Coulomb's law: F = k·q₁·q₂/r², with k ≈ 8.99×10⁹ N·m²/C²; force is attractive for unlike charges, repulsive for like charges.

Elementary charge e = 1.602×10⁻¹⁹ C; one coulomb equals the charge of about 6.24×10¹⁸ electrons.

Electron mass 9.11×10⁻³¹ kg, roughly 1/1836 of proton mass; the nucleus holds nearly all atomic mass.

Atomic number Z = number of protons; neutral atom has equal electrons, so net charge is zero.

Valence electrons occupy the outermost shell; 1–3 valence electrons indicate a conductor, 5–8 an insulator.

In a solid conductor, current is carried by electron drift opposite to conventional current direction.

Ionization removes electrons from atoms, producing free electrons plus positive ions and enabling conduction in gases.

Energy levels are quantized shells (K, L, M, N); an electron absorbing a photon jumps to a higher shell.

Charging methods: friction (triboelectric transfer), conduction (contact, shared charge), induction (no contact, opposite charge near the inducing body).

Like charges repel, unlike attract; the force acts along the line joining the charges.

Static charge resides on the outer surface of a conductor and distributes so the internal field is zero.

Pointed conductors concentrate charge density; corona discharge occurs where the local field exceeds air breakdown (~3×10⁶ V/m).

Conductors: metals, carbon, electrolytes; insulators: glass, rubber, dry air, plastics.

Bonding connects two conductors to equalize potential; earthing connects to ground to drain static charge safely.

Static discharge risk is controlled by conductive flooring, wrist straps, and humidity control, not by insulating the charged item.

Semiconductors (silicon, germanium) conduct only when doped or energized; their resistance falls with temperature.

Current I in amperes = rate of charge flow, I = Q/t; 1 A = 1 C/s.

Voltage V (potential difference) in volts = energy per unit charge, V = W/Q; 1 V = 1 J/C.

Resistance R in ohms; 1 Ω passes 1 A when 1 V is applied.

EMF is the source's open-circuit potential; terminal voltage equals EMF minus internal drop I·r.

Conductance G = 1/R, in siemens (S).

Charge Q in coulombs = I·t; energy W in joules = V·I·t.

Conventional current flows from positive to negative externally; electron flow is the reverse.

Ammeter connects in series with low resistance; voltmeter connects in parallel with high resistance.

Six practical methods: friction, pressure (piezoelectric), heat (thermocouple), light (photovoltaic), chemical action, and magnetism.

Faraday's law: induced EMF E = −N·dΦ/dt; magnitude depends on turns, flux change, and rate of change.

Lenz's law: induced current opposes the change producing it, giving the negative sign.

Generator EMF: E = B·l·v for a conductor moving perpendicular to a uniform field.

AC generator: E = B·A·N·ω·sin(ωt), peak EMF = B·A·N·ω.

Piezoelectric effect generates EMF when quartz or certain crystals are strained.

Thermocouples generate small EMFs (microvolts per °C) from the Seebeck effect between dissimilar metals.

Photovoltaic cells convert light directly to EMF using semiconductor junctions.

Primary cells are not rechargeable (carbon-zinc, alkaline, mercury); secondary cells are rechargeable (lead-acid, NiCd, lithium-ion).

Lead-acid cell nominal EMF ≈ 2.1 V per cell; a 12 V battery has six cells in series.

Cell EMF depends on electrode and electrolyte materials, not on cell size; capacity depends on electrode area and mass.

Series connection adds EMFs: E_total = E₁ + E₂ + …; current capacity equals the weakest cell.

Parallel connection keeps EMF at one cell value; capacities add: C_total = C₁ + C₂ + ….

Internal resistance causes terminal voltage V = E − I·r; it rises as the cell ages or discharges.

Battery capacity in ampere-hours: Ah = current (A) × discharge time (h).

Thermocouples, photovoltaic cells, and DC generators are DC sources other than chemical cells.

Ohm's law: V = I·R; rearranged I = V/R and R = V/I.

Series: R_total = R₁ + R₂ + …; current is common; voltages add.

Parallel: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is common; currents add.

Two resistors in parallel: R = (R₁·R₂)/(R₁ + R₂).

Kirchhoff's current law: sum of currents into a node equals sum out (ΣI = 0).

Kirchhoff's voltage law: algebraic sum of EMFs and drops around a closed loop is zero.

Voltage divider: V_out = V_in · R₂/(R₁ + R₂) for a series pair.

Maximum power transfer to a load occurs when load resistance equals source internal resistance.

R = ρ·l/A; resistance rises with length and resistivity, falls with cross-sectional area.

Temperature coefficient: R = R₀[1 + α(T − T₀)]; metals have positive α, carbon and semiconductors negative.

Resistor colour code digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9.

Gold band = ±5%, silver = ±10%, brown = ±1%, red = ±2%; no band = ±20%.

Series resistors add directly; parallel combination is always less than the smallest resistor.

A potentiometer is a three-terminal variable resistor used as a voltage divider; a rheostat is a two-terminal variable resistor.

Power rating: P = I²R must not be exceeded or the resistor overheats; derate with ambient temperature.

A thermistor's resistance changes markedly with temperature; an LDR's resistance falls with increasing light.

P = V·I = I²R = V²/R; unit is the watt (1 W = 1 J/s).

Energy W = P·t; 1 kWh = 3.6×10⁶ J.

Efficiency η = useful output power / input power × 100%.

Power dissipated in a resistor equals the heat produced; total power in a series circuit P = I²·R_total.

In parallel branches, total power is the sum of branch powers: P = V²/R₁ + V²/R₂ + ….

Source power delivered equals EMF × current; internal loss is I²·r, so output power = E·I − I²·r.

Maximum power transfer occurs at R_load = r, where efficiency is only 50%.

Three-phase power: P = √3·V_L·I_L·cos φ for balanced loads.

C = Q/V; unit farad (F); 1 F = 1 C/V.

Parallel-plate: C = ε₀·ε_r·A/d, with ε₀ = 8.854×10⁻¹² F/m.

Capacitors in parallel add: C_total = C₁ + C₂; in series: 1/C_total = 1/C₁ + 1/C₂.

Energy stored: W = ½·C·V² = ½·Q·V = Q²/(2C).

Time constant τ = R·C; after one τ a capacitor charges to 63.2% and discharges to 36.8% of final value.

Capacitive reactance X_C = 1/(2πfC); it falls as frequency rises.

Capacitors block DC and pass AC; voltage across a capacitor cannot change instantaneously.

Dielectric strength limits working voltage; breakdown punctures the dielectric and shorts the plates.

Magnetic flux Φ in webers; flux density B = Φ/A in teslas (1 T = 1 Wb/m²).

Magnetomotive force F = N·I (ampere-turns); magnetizing force H = N·I/l (A/m).

Permeability of free space μ₀ = 4π×10⁻⁷ H/m; relative permeability μ_r = μ/μ₀.

Force on a current-carrying conductor: F = B·I·l·sin θ.

Field around a straight conductor: B = μ₀·I/(2πr); direction given by the right-hand grip rule.

Solenoid field: B = μ₀·μ_r·N·I/l; adding an iron core raises flux greatly.

Curie point: ferromagnetic materials lose their magnetism above a critical temperature (e.g., iron ~770 °C).

Hard magnetic materials (steel) retain magnetism; soft materials (soft iron) are easily magnetized and demagnetized.

Self-induced EMF: E = −L·dI/dt; inductance L in henries (1 H = 1 V·s/A).

Solenoid inductance: L = μ₀·μ_r·N²·A/l.

Inductors in series add; in parallel: 1/L_total = 1/L₁ + 1/L₂.

Energy stored: W = ½·L·I².

Inductive reactance X_L = 2πfL; it rises with frequency.

Time constant τ = L/R; current reaches 63.2% of final value after one τ.

Inductors oppose changes in current; current cannot change instantaneously.

Mutual inductance between coils depends on turns, geometry, and coupling coefficient k (0 ≤ k ≤ 1).

RMS = peak/√2 ≈ 0.707 × peak; peak = RMS × 1.414; average of a full sine is zero.

Frequency f = 1/T; angular frequency ω = 2πf.

Impedance: Z = √(R² + (X_L − X_C)²); phase angle φ = arctan[(X_L − X_C)/R].

Resonance when X_L = X_C, so f_r = 1/(2π√(LC)); impedance is minimum and current maximum in series resonance.

Power: true P = V·I·cos φ (watts), reactive Q = V·I·sin φ (VAR), apparent S = V·I (VA).

Power factor = cos φ = R/Z; corrected by adding parallel capacitance to cancel inductive VARs.

In a purely inductive circuit current lags voltage by 90°; in a purely capacitive circuit current leads by 90°.

Three-phase star: V_L = √3·V_ph; delta: I_L = √3·I_ph.

Form factor = RMS/average = 1.11 for a sine wave; crest factor = peak/RMS = 1.414.

A rectified full-wave sine has average value 2·V_peak/π ≈ 0.637·V_peak.

A hot-wire or true-RMS meter reads correct RMS for non-sinusoidal waveforms; a rectifier meter is calibrated for sine only.

A square wave has RMS equal to its peak value and form factor 1.0.

A triangular wave has RMS = peak/√3 ≈ 0.577 × peak.

Instantaneous value of a sine: v = V_peak·sin(2πft + φ).

Two waveforms in phase have zero phase difference; a phase difference of 180° means complete opposition.

Frequency measurement via oscilloscope: f = 1/(time per division × divisions per cycle).