Electromagnetic Induction and Alternating Currents
Electromagnetic induction and alternating currents tests Faraday and Lenz laws, self and mutual inductance, AC behaviour of resistors, inductors, and capacitors, series LCR resonance, power, and transformers. The exam frequently combines flux changes with phase and impedance reasoning.
Core rules and concepts
- Magnetic flux Phi = BA cos(theta). Induced emf = -N dPhi/dt; the minus sign is Lenz law, opposing the change in flux.
- Motional emf for a rod moving perpendicular to B is B l v.
- Self-induced emf = -L dI/dt; energy stored in an inductor = 1/2 LI^2. Mutual inductance relates flux in one coil to current in another.
- AC quantities use rms values: I_rms = I_peak/sqrt(2). Reactance X_L = omega L and X_C = 1/(omega C).
- Series LCR impedance Z = sqrt(R^2 + (X_L - X_C)^2); current I = V/Z. Resonance occurs when X_L = X_C, giving omega = 1/sqrt(LC), minimum Z, and maximum current.
- Average power P = V_rms I_rms cos(phi), where cos(phi) is power factor. A transformer changes voltage in ratio N_s/N_p and is efficient only for AC.
Worked example
A 200-turn coil of area 0.020 m^2 has B changing from 0.10 T to 0.50 T in 0.20 s, perpendicular to the coil. Change in flux is (0.40)(0.020) = 0.0080 Wb. Induced emf magnitude is N(Delta Phi/Delta t) = 200 x 0.0080/0.20 = 8.0 V.
Traps that cost marks
- Confusing flux with emf; a constant flux gives zero emf.
- Dropping the Lenz minus sign when asking for direction.
- Using peak instead of rms values in power calculations.
- Saying a transformer works on steady DC.
- Forgetting that at resonance X_L and X_C cancel but are not zero.