Electrical engineering

Capacitors, inductors, AC

Charge/discharge, reactance, impedance, resonance.

Basics

C and L

A capacitor stores charge (electric field) and resists sudden voltage change. An inductor stores energy in a magnetic field and resists sudden current change. In DC steady state, C looks open, L looks short.

AC and RMS

Mains is sinusoidal AC. RMS is the DC value that would give the same average power in a resistor. For a sine, V_rms = V_peak / √2.

Formulas

Capacitor

Q = C V, i = C dV/dt

C in farads. Parallel: C adds. Series: 1/C adds.

Symbols

C capacitance (F)
Q charge (C)

Inductor

v = L di/dt, U = ½ L I²

L in henrys. Voltage appears when current is changing.

Symbols

L inductance (H)

RC time constant

τ = R C, v(t) = v_∞ + (v₀ − v_∞) e^{−t/τ}

After about 5τ the transient is essentially over.

Symbols

τ time constant (s)

Reactance

X_C = 1 / (ω C), X_L = ω L, ω = 2π f

C passes high frequency; L passes low frequency.

Symbols

ω angular frequency (rad/s)
X reactance (Ω)

Impedance

Z = R + j X, |Z| = √(R² + X²)

AC Ohm: Ṽ = Ĩ Z, including phase.

Symbols

j imaginary unit

LC resonance

f₀ = 1 / (2π √(L C))

Series: |Z| minimum. Parallel: |Z| maximum.

Symbols

f₀ resonant frequency

Sine RMS

V_rms = V_peak / √2 ≈ 0.707 V_peak

Nominal 220 V single-phase in Korea is RMS.

In this field

Electrical engineering

DC circuits

Ohm, Kirchhoff, series/parallel, power.

Electrical engineering

Power, semiconductors, digital

Transformers, three-phase, diodes, gates.

Electrical engineering

Magnetism, motors, control

Faraday, motors, filters, feedback.

Electrical engineering

Signals and logic

Fourier sketch, sampling, Boolean algebra.

Electrical engineering

Semiconductors

Carriers, diodes, a MOSFET sketch.

Electrical engineering

Measurements and electrical safety

Multimeters, RMS versus peak, transformer ratio, and electrical safety.

Electrical engineering

Op-amps and filters

The ideal op-amp, inverting and non-inverting gain, RC low- and high-pass, cutoff frequency.

Electrical engineering

Digital logic

Boolean algebra, gates, flip-flops, and timing.

Electrical engineering

Three-phase power

Line versus phase, Y and Δ, √3 power, and a motor sketch.

Electrical engineering

Batteries and photovoltaics

Capacity and C-rate, series/parallel packs, PV I–V curves, and the maximum-power point.