Electromagnetic Induction and Alternating Currents
What the exam tests
This domain combines Faraday law, Lenz law, motional emf, self and mutual inductance, AC through R, L and C, series LCR resonance, power factor and transformers. Numerical questions often ask impedance, current, resonance frequency or turns ratio.
Core rules
- Magnetic flux Φ = BA cosθ. Induced emf ε = −dΦ/dt; the minus sign expresses Lenz law.
- Motional emf for a rod moving perpendicular to B is ε = Blv.
- Self-induced emf ε = −L dI/dt; energy stored in an inductor U = 1/2 LI^2. Mutual inductance relates flux in one coil to current in another.
- For sinusoidal AC, RMS current I_rms = I0/√2; average current over a full cycle is zero.
- Reactance X_L = ωL and X_C = 1/(ωC). Impedance Z = √(R^2 + (X_L − X_C)^2).
- At resonance X_L = X_C, so Z is minimum and current is maximum; f = 1/(2π√(LC)).
- Transformer: Vs/Vp = Ns/Np for an ideal transformer; power is conserved, frequency is unchanged.
Worked example
A series LCR circuit has R = 30 Ω, X_L = 50 Ω and X_C = 20 Ω across 120 V RMS. Then Z = √(30^2 + 30^2) = 42.4 Ω. RMS current is 120/42.4 = 2.83 A. Power dissipated is I^2R = (2.83)^2×30 ≈ 240 W. The net reactance is inductive because X_L exceeds X_C.
Traps
Lenz law opposes the change in flux, not the flux itself. The average of sinusoidal AC over a full cycle is zero, but RMS is not zero. Use RMS values for power in resistive parts. At resonance impedance is minimum, not maximum. A transformer changes voltage and current but not frequency or power in the ideal case.