Electromagnetic Induction and Alternating Current
Electromagnetic Induction and Alternating Current tests changing flux, Lenz's law, self- and mutual inductance, AC circuits with R, L and C, resonance, power factor and transformers.
Core rules
- Faraday's law: ε = -N dΦ/dt. The minus sign is Lenz's law: induced current opposes the change producing it.
- Self-induced emf ε = -L di/dt; energy stored in an inductor = ½Li². Mutual inductance depends on coupling and geometry.
- For AC, I_rms = I₀/√2, V_rms = V₀/√2. Reactances: X_L = ωL, X_C = 1/(ωC).
- Series LCR impedance Z = √(R² + (X_L - X_C)²). Resonance occurs at ω = 1/√(LC), when Z = R and current is maximum.
- Transformer: V_s/V_p = N_s/N_p. An ideal transformer conserves power; a step-up transformer raises voltage and lowers current.
Worked example
A 200-turn coil of area 0.020 m² has a perpendicular magnetic field reduced from 0.50 T to 0.10 T in 0.10 s. Flux change per turn = 0.020(0.40) = 8.0×10⁻³ Wb. Induced emf magnitude = NΔΦ/Δt = 200(8.0×10⁻³)/0.10 = 16 V.
Traps
Dropping the minus sign in Faraday's law when the question asks direction; mixing peak and rms values; assuming resonance gives zero impedance (it gives minimum Z = R); and treating a real transformer as 100% efficient unless told to.