Transformers/inductors (as applicable) - Physics 2 AP Study Notes

Transformers are devices that change alternating voltage from one value to another using electromagnetic induction. A transformer consists of two coils—the primary coil (input) and secondary coil (output)—wound around a soft iron core.

Key Principle: When alternating current flows through the primary coil, it creates a changing magnetic field in the iron core. This changing flux induces an EMF in the secondary coil via Faraday's Law of Electromagnetic Induction.

Essential Equations:

Transformer Equation: $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

Where Vₚ = primary voltage, Vₛ = secondary voltage, Nₚ = number of turns on primary, Nₛ = number of turns on secondary.

Power Relationship (for ideal transformers): $$V_p I_p = V_s I_s$$

Or: $$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$

Step-up transformer: Nₛ > Nₚ, increases voltage, decreases current

Step-down transformer: Nₛ < Nₚ, decreases voltage, increases current

Efficiency: $$\text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100% = \frac{V_s I_s}{V_p I_p} \times 100%$$

Energy Losses: Real transformers lose energy through:

• Resistance heating in coils (I²R losses)
• Eddy currents in the core (minimized by laminating the core)
• Magnetic flux leakage
• Hysteresis (magnetization/demagnetization)

Cambridge Definition: A transformer is an electrical device that uses electromagnetic induction to change an alternating voltage to a different value. The soft iron core links magnetic flux between coils efficiently.

Power Transmission Analogy: Think of transformers like gear systems on a bicycle. Step-up transformers are like shifting to a higher gear—you pedal less frequently (lower current) but go faster (higher voltage). Step-down transformers are the opposite—more frequent pedaling (higher current) but easier effort per stroke (lower voltage).

Real-World Application 1: National Grid Electricity is generated at power stations at ~25,000V. Step-up transformers increase this to 400,000V for transmission. Why? Power loss in cables = I²R. By increasing voltage and proportionally decreasing current, transmission losses drop dramatically. Near homes, step-down transformers at substations reduce voltage to 230V for safe domestic use.

Real-World Application 2: Phone Chargers Your phone charger contains a step-down transformer converting 230V mains to 5-12V DC (after rectification). The transformer ensures safe, low voltage reaches sensitive electronics.

Real-World Application 3: Welding Equipment Welding machines use step-down transformers to convert mains voltage to very low voltage (~50V) but extremely high current (100-300A) needed to melt metal.

Why AC Only? Transformers require changing magnetic flux. Direct current (DC) produces steady flux, inducing no EMF in the secondary coil. Only alternating current creates the oscillating magnetic field necessary for induction.

The Iron Core's Role: Soft iron has high magnetic permeability, concentrating magnetic field lines. It magnetizes and demagnetizes easily with AC, efficiently channeling flux from primary to secondary. Lamination (thin insulated layers) prevents large eddy currents forming circular paths within the core.