AC Circuits

DC vs AC, the sinusoidal waveform, amplitude / peak / peak-to-peak / RMS, period, frequency, angular frequency.

Rotating phasor view of AC, sine vs cosine, phase angle, comparing two waveforms on the same time axis.

Structure, the parallel-plate formula, Q = CV, series / parallel combination rules, and RC charging / discharging with the time constant τ = RC.

X_C = 1/(ωC), I leads V by 90° in a pure capacitor, frequency dependence, applications in coupling / bypass / filtering.

Coil structure, L, flux linkage Ψ = LI, back-EMF v = L · dI/dt, energy ½LI², series / parallel (mirror of resistors), and LR energise / de-energise with the time constant τ = L/R.

X_L = ωL, V leads I by 90° in a pure inductor, magnetism basics (H = NI/l, B = μH), transformer principle V₁/V₂ = N₁/N₂ and why cores are laminated.

Rotating phasors on the complex plane, polar and rectangular forms, phasor addition, and the jω shortcut that turns AC calculus into algebra.

Complex impedance Z = R + jX, impedance triangles, voltage phasor diagrams, and the frequency flip from net capacitive to net inductive through resonance.

Transfer function H(jω), Bode magnitude plots, first-order RC and RL filters (low-pass and high-pass), cutoff frequency, and a preview of band-pass RLC.

Resonant frequency f₀ = 1/(2π√(LC)), the Q factor, bandwidth = f₀/Q, series vs parallel RLC, and the trade-off between selectivity and passband width.