Section A: Electromagnetic Induction (Faraday & Lenz)

Magnetic flux Φ = BA cos θ measures how much of a magnetic field B passes through a surface of area A at angle θ to the field direction. Its SI unit is the Weber (Wb). Faraday's first law states that any change in flux through a circuit induces an EMF; Faraday's second law quantifies this: EMF = −dΦ/dt. The magnitude equals the rate of flux change; the negative sign is Lenz's law — the induced EMF drives a current that opposes the flux change responsible for it. This is a statement of energy conservation: energy input (mechanical work) equals energy output (electrical).

Section B: Motional EMF and the Rotating Coil

When a conductor of length l moves with velocity v perpendicular to field B, charges experience Lorentz force F = qvB, creating motional EMF ε = Bvl. Polarity is determined by F = qv × B (right-hand rule). For a coil rotating at angular velocity ω in field B: ε = NBAω sin(ωt), with peak EMF ε_{0} = NBAω. This is the operating principle of all AC generators.

Section C: Self and Mutual Inductance

Self-inductance L quantifies a coil's opposition to changes in its own current: ε = −L(dI/dt). For a solenoid: L = μ_{0}$n^{2}$Al. Energy stored: U = ½$LI^{2}$ (in the magnetic field). Mutual inductance M between two coils: ε_{2} = −M(d$I_{1}$/dt); for coaxial solenoids M = μ_{0}n_{1}n_{2}Al. Eddy currents (induced in bulk conductors) cause heating — exploited in induction furnaces, electromagnetic braking, and speedometers — and are minimized by lamination in transformer cores.

Section D: AC Fundamentals and Single-Element Circuits

AC voltage v = $V_{0}$ sin(ωt) has V_rms = $V_{0}$/√2 (for power calculations) and V_mean = 2$V_{0}$/π (half-cycle average). In pure R: V and I in phase, P = V_rms I_rms. In pure L (X_L = ωL): current lags voltage by 90°, P = 0. In pure C (X_C = 1/ωC): current leads voltage by 90°, P = 0. Mnemonic: ELI the ICE man.

Section E: Series LCR Circuit and Resonance

Impedance Z = √($R^{2}$ + (X_L − X_C)^{2}); phase angle tan φ = (X_L − X_C)/R. At resonance (X_L = X_C): f_{0} = 1/(2π√LC), Z = R (minimum), I = V/R (maximum), φ = 0. Average power P = V_rms I_rms cos φ = I_r$ms^{2}$ R; power factor cos φ = R/Z. Wattless current = I_rms sin φ.

Section F: Transformer

Turns ratio: V_s/V_p = N_s/N_p. Current ratio (INVERSE): I_s/I_p = N_p/N_s. Ideal transformer: P_in = P_out. Real losses: copper ($I^{2}$R), eddy currents (lamination reduces this), hysteresis (soft iron reduces this), flux leakage. High-voltage transmission uses step-up transformers to minimize $I^{2}$R losses over long distances; step-down transformers restore household voltages.