Electromagnetic Induction and Alternating Currents

The One Thing

Changing magnetic flux produces an induced emf, while inductance opposes changes in current and stores energy magnetically. These principles explain AC circuit behaviour, resonance, and transformer operation through mutual induction.

Reactions, Processes and Experiments

Key Terms

• Magnetic flux: The amount of magnetic field passing through a surface; for a uniform field, Φ = BA cos θ.
• Faraday’s law of electromagnetic induction: The induced emf is proportional to the negative rate of change of magnetic flux: ε = -N dΦ/dt.
• Lenz’s law: The induced current flows in a direction that opposes the change in magnetic flux responsible for producing it.
• Motional emf: The emf produced when a conductor moves through a magnetic field, commonly given by ε = Bℓv when motion is perpendicular to the field.
• Eddy currents: Circulating currents induced in bulk conductors exposed to changing magnetic fields; they may cause heating or magnetic damping.
• Self-inductance: The property of a coil by which a change in its own current induces an opposing emf: ε = -L dI/dt.
• Mutual inductance: The property by which a changing current in one coil induces an emf in a nearby coil: ε₂ = -M dI₁/dt.
• Inductor: A circuit component, usually a coil, that opposes changes in current and stores energy in its magnetic field.
• Energy stored in an inductor: The energy stored in the magnetic field of an inductor: U = 1/2 LI².
• Alternating current: A current whose magnitude and direction vary periodically, commonly represented as i = I₀ sin(ωt + φ).
• Peak and rms values: For a sinusoidal current, I_rms = I₀/√2 and V_rms = V₀/√2; rms values produce the same heating effect as equivalent DC values.
• Reactance: The opposition offered by an inductor or capacitor to AC: X_L = ωL and X_C = 1/(ωC).
• Impedance: The total opposition to AC; for a series RLC circuit, Z = √[R² + (X_L - X_C)²].
• Phase difference: The angular difference between voltage and current; current is delayed in an inductor and advanced in a capacitor.
• Power factor: The ratio of average power to apparent power, given by cos φ; in a series RLC circuit, cos φ = R/Z.
• Resonance: The condition in a series RLC circuit when X_L = X_C, giving minimum impedance, maximum current, and resonant frequency f₀ = 1/(2π√LC).
• Transformer: A device that changes AC voltage using mutual induction between primary and secondary coils.
• Step-up transformer: A transformer with more turns in the secondary coil than in the primary coil, increasing voltage while decreasing current ideally.
• Step-down transformer: A transformer with fewer turns in the secondary coil than in the primary coil, decreasing voltage while increasing current ideally.
• Transformer equation: For an ideal transformer, V_s/V_p = N_s/N_p = I_p/I_s, and input power equals output power.

Easily Confused

• Self-inductance and mutual inductance: Self-inductance involves a coil inducing an opposing emf in itself; mutual inductance involves one coil inducing an emf in a nearby second coil.
• Induced emf and induced current: A changing magnetic flux produces emf, but current flows only if the circuit provides a conducting closed path.
• Inductive reactance and capacitive reactance: X_L = ωL increases with frequency, whereas X_C = 1/(ωC) decreases with frequency.
• Peak and rms values: Peak values are the maximum instantaneous values; rms values are the equivalent DC values for heating.
• Step-up and step-down transformers: A step-up transformer has N_s > N_p and increases voltage; a step-down transformer has N_s < N_p and decreases voltage.
• Resistance and reactance: Resistance dissipates energy as heat, whereas ideal reactance temporarily stores and returns energy.
• Lenz’s law and Faraday’s law: Faraday’s law gives the magnitude and sign of induced emf, while Lenz’s law explains that the induced effect opposes the change producing it.
• Transformer operation with AC and DC: A transformer requires changing current and therefore operates with AC; it does not work continuously with steady DC.
• Resonance and maximum impedance: In a series RLC circuit, resonance occurs when X_L = X_C, producing minimum impedance and maximum current.

What Gets Asked

• Calculate magnetic flux using Φ = BA cos θ and identify whether a change in field, area, orientation, or relative motion produces induction. The main mark-losing error is using the wrong angle: θ is measured between the magnetic field and the normal to the surface.
• Apply Faraday’s law, ε = -N dΦ/dt, and explain the negative sign using Lenz’s law. Omitting the negative sign or failing to state that the induced effect opposes the change loses the interpretation mark.
• Calculate motional emf using ε = Bℓv for a rod whose length, velocity, and magnetic field are mutually perpendicular. Do not use this expression without the stated perpendicular arrangement.
• Analyse a series RLC circuit using X_L = ωL, X_C = 1/(ωC), Z = √[R² + (X_L - X_C)²], tan φ = (X_L - X_C)/R, and P = V_rms I_rms cos φ. Common slips include reversing whether current leads or lags and treating reactance as dissipated power.
• Identify resonance using X_L = X_C, f₀ = 1/(2π√LC), Z = R, and maximum current. The key distinction is that resonance gives minimum impedance, not maximum impedance.
• Solve transformer problems using V_s/V_p = N_s/N_p = I_p/I_s and V_p I_p = V_s I_s. The main errors are reversing the turns ratio or stating that a step-up transformer increases both voltage and current.