Electromagnetic Induction and Alternating Current
What this domain tests
Electromagnetic Induction and Alternating Current tests Faraday's law, Lenz's law, self and mutual inductance, AC through R, L and C, series LCR resonance, power factor and transformers.
Core rules
- Induced EMF ε = −dΦ/dt; Lenz's law fixes the direction so as to oppose the flux change.
- Motional EMF ε = Bvl for a rod moving perpendicular to B.
- Self-inductance ε = −L dI/dt; energy = ½LI². Mutual inductance couples two coils through flux linkage.
- AC: I_rms = I_peak/√2, V_rms = V_peak/√2; the average of a sine over a cycle is zero.
- Reactances X_L = ωL, X_C = 1/ωC; impedance Z = √(R² + (X_L − X_C)²).
- Resonance at ω = 1/√(LC): Z minimum, current maximum, power factor 1.
Worked example
A series LCR circuit has R = 30 Ω, X_L = 40 Ω and X_C = 80 Ω, connected to 200 V (rms). Z = √(30² + (−40)²) = 50 Ω, so I_rms = 200/50 = 4 A. Average power P = I_rms²R = 16 × 30 = 480 W. The circuit is capacitive because X_C > X_L, so current leads voltage.
Traps
- Using peak values in power formulas instead of rms values.
- Dropping the minus sign in Lenz's law.
- Assuming average AC power is always zero; it is zero only for pure L or pure C.
- Thinking a transformer changes frequency or power; it changes voltage and current.