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Part of MAG-02 — Electromagnetic Induction & Alternating Current

Cheat Sheet — Final Revision

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MAG-02 Master Cheat Sheet

Core Laws

Law	Formula	Note
Faraday	EMF = −N(dΦ/dt)	−ve sign = Lenz's law
Lenz	I_induced opposes $\Delta$ Φ	Consequence of energy conservation
Motional EMF	ε = Bvl	v ⊥ B ⊥ l; polarity: F = qv×B

Self and Mutual Inductance

Quantity	Formula	Unit
Self-inductance (general)	ε = −L(dI/dt)	H
Solenoid	L = μ_{0} $n^{2}$ Al = μ_{0} $N^{2}$ A/l	H
Mutual inductance	ε_{2} = −M(d $I_{1}$ /dt)	H
Coaxial solenoids	M = μ_{0}n_{1}n_{2}Al	H
Inductor energy	U = ½ $LI^{2}$	J
Rotating coil peak	ε_{0} = NBAω	V

AC Circuits — Quick Reference

Element	Reactance	Phase (I vs V)	Power
R	R	In phase	P = V_rms I_rms
L	X_L = ωL	I lags 90° (ELI)	0
C	X_C = 1/ωC	I leads 90° (ICE)	0
LCR	Z = √( $R^{2}$ +(X_L−X_C)^{2})	tan φ = (X_L−X_C)/R	V_rms I_rms cos φ

Resonance

$f_0 = \frac{1}{2\pi\sqrt{LC}} \qquad Z = R\,(\text{min}) \qquad \phi = 0 \qquad I = \frac{V}{R}\,(\text{max})$

AC Values

$V_\text{rms} = \frac{V_0}{\sqrt{2}} \approx 0.707\,V_0 \qquad V_\text{mean} = \frac{2V_0}{\pi} \approx 0.637\,V_0$

Transformer

$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \qquad \eta = \frac{P_s}{P_p} = \frac{V_s I_s}{V_p I_p}$

Critical Traps (Never Forget)

Resonance: Z = R (NOT zero)
Transformer current: I ratio is INVERSE of N ratio
Voltages in LCR: phasor addition, NOT arithmetic sum
ELI the ICE man for phase relationships
Lamination → reduces eddy currents (NOT hysteresis)
Soft iron → reduces hysteresis loss (NOT eddy currents)
Average power over full AC cycle: only $I^{2}$ R term survives

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