Electromagnetic Induction and Alternating Currents
This domain links changing magnetic flux to induced emf and extends circuit analysis to alternating current. Expect numerical work on inductance, impedance, resonance and transformers.
Core rules and concepts
- Faraday’s law: ε = −dΦ/dt; for N turns ε = −N dΦ/dt. Lenz’s law gives the direction: the induced current opposes the change in flux.
- Self-inductance ε = −L dI/dt; energy stored U = ½LI². Mutual inductance ε2 = −M dI1/dt.
- For AC: I_rms = I0/√2, V_rms = V0/√2. Reactances X_L = ωL and X_C = 1/ωC.
- Series RLC impedance Z = √[R² + (X_L − X_C)²]; current I = V/Z; power factor cosφ = R/Z.
- Resonance occurs when X_L = X_C, so f = 1/(2π√LC); impedance is minimum and current maximum.
- Transformer: Vs/Vp = Ns/Np; ideal power is conserved, so VpIp = VsIs. Frequency is unchanged.
Worked example
A series circuit has R = 30 Ω and X_L = 40 Ω across a 200 V AC supply. Find Z, current, power factor and power. Z = √(30² + 40²) = 50 Ω. I = 200/50 = 4 A. Power factor = R/Z = 30/50 = 0.6. Power = I²R = (4²)(30) = 480 W.
Traps
- Lenz’s law gives direction only; use Faraday’s law for magnitude.
- Average AC voltage over a full cycle is zero, but RMS voltage is not zero.
- At resonance X_L and X_C cancel; they are not zero individually.
- A transformer changes voltage and current, not frequency or power in an ideal case.
- Eddy currents are reduced by laminations, not by increasing core thickness.