Electromagnetic Induction and Alternating Currents
What this domain tests
This domain pairs Faraday–Lenz induction and self/mutual inductance with AC circuits: phasors, impedance, resonance, power factor and transformers.
Core rules
- ε = −N dΦ/dt, with Φ = BA cosθ. The minus sign is Lenz's law: the induced current opposes the change in flux. Emf is maximum when the coil plane is parallel to B, where flux is zero but changing fastest.
- Self-induced emf ε = −L dI/dt, with inductor energy U = ½LI²; mutual inductance gives ε₂ = −M dI₁/dt.
- AC: I_rms = I₀/√2 and V_rms = V₀/√2; the full-cycle average of a pure sine is zero.
- Series LCR: Z = √[R² + (X_L − X_C)²], tanφ = (X_L − X_C)/R; at resonance f = 1/(2π√LC), Z = R and the power factor is 1.
- P = V_rms I_rms cosφ. Transformer: V_s/V_p = N_s/N_p, ideal power conserved, frequency unchanged.
Worked example
A series LCR circuit has R = 30 Ω, X_L = 70 Ω and X_C = 30 Ω across a 200 V (rms) supply. Find Z, the rms current and the power. X_L − X_C = 40 Ω, so Z = √(30² + 40²) = 50 Ω. I_rms = 200/50 = 4 A. P = I²R = 16 × 30 = 480 W. Power is dissipated only in R; the reactances store and return energy each cycle.
Traps that cost marks
- Substituting peak values into P = V I cosφ instead of rms values.
- Claiming resonance makes current zero - it makes Z minimum and current maximum.
- Ignoring Lenz's law when asked for the direction of induced current.
- Expecting a transformer to change frequency or to work on steady DC.