Electrical engineering
DC circuits
Ohm, Kirchhoff, series/parallel, power.
Basics
Ohm's law
For many resistors, V=IR. Current is charge flow (A=C/s), voltage is energy per charge (V=J/C), resistance is opposition (Ω). Passive sign: current enters the + terminal of the element.
Kirchhoff
KCL: algebraic sum of currents at a node is 0 (charge). KVL: algebraic sum of voltages around a loop is 0 (energy). The two pillars of circuit analysis.
Series and parallel
Series: same current, resistances add, voltage divides. Parallel: same voltage, conductances add, current divides. Household outlets are parallel so each load sees the same voltage.
Formulas
Ohm's law
The defining relation for a linear resistor.
Symbols
-
Vvoltage (V) -
Icurrent (A) -
Rresistance (Ω)
Series resistance
The same current flows through each.
Parallel resistance
For two: R_eq = R₁ R₂ / (R₁+R₂).
Voltage divider
Across R₂ in series. A heavy load throws it off.
Power
Instantaneous power dissipated in a resistor. Unit W.
Symbols
-
Ppower (W)
Resistance and resistivity
Longer, thinner, higher ρ → more R. Resistivity depends on temperature.
Symbols
-
ρresistivity (Ω·m) -
Llength -
Across-section area
In this field
Capacitors, inductors, AC
Charge/discharge, reactance, impedance, resonance.
Power, semiconductors, digital
Transformers, three-phase, diodes, gates.
Magnetism, motors, control
Faraday, motors, filters, feedback.
Signals and logic
Fourier sketch, sampling, Boolean algebra.
Semiconductors
Carriers, diodes, a MOSFET sketch.
Measurements and electrical safety
Multimeters, RMS versus peak, transformer ratio, and electrical safety.
Op-amps and filters
The ideal op-amp, inverting and non-inverting gain, RC low- and high-pass, cutoff frequency.
Digital logic
Boolean algebra, gates, flip-flops, and timing.
Three-phase power
Line versus phase, Y and Δ, √3 power, and a motor sketch.
Batteries and photovoltaics
Capacity and C-rate, series/parallel packs, PV I–V curves, and the maximum-power point.