5.2 Transformers

Device that transfers electrical energy from one circuit to another through electromagnetic induction, usually with a change in voltage and current.
Ideal Transformer Equations:
- Voltage Ratio: $V_1/V_2 = N_1/N_2 = a$ (turns ratio, $a > 1$ for step-down, $a < 1$ for step-up).
- Current Ratio: $I_2/I_1 = N_1/N_2 = a$.
- Impedance Transformation: $Z_{in} = (N_1/N_2)^2 Z_L = a^2 Z_L$.
- Power: $V_1 I_1 = V_2 I_2$ (input power = output power, no losses).
Practical Transformer: Includes losses and non-ideal characteristics.
- Losses:
  - Core Losses: Due to alternating flux in the core.
    - Hysteresis Loss: Energy lost in reversing magnetic domains (related to area of B-H loop).
    - Eddy Current Loss: Circulating currents induced in the core material (reduced by laminating core).
  - Copper Losses ($P_{cu}$): $I^2R$ losses in primary and secondary windings. $P_{cu} = I_1^2 R_1 + I_2^2 R_2$.
- Equivalent Circuit: Represents resistances, leakage reactances, and magnetizing branch (core losses and magnetizing reactance). Typically referred to primary or secondary side.
- Efficiency ($\eta$): $\eta = (P_{out} / P_{in}) \times 100\% = (P_{out} / (P_{out} + P_{losses})) \times 100\%$.
  - Maximum efficiency occurs when copper losses equal core losses.
- Voltage Regulation (VR): Measures the change in secondary voltage from no-load to full-load conditions.
  - $VR = ((V_{no-load} - V_{full-load}) / V_{full-load}) \times 100\%$.
  - Lower VR is better.
Autotransformer: A transformer with a single winding that acts as both primary and secondary.
- Part of the winding is common to both circuits.
- Advantages: Smaller size, higher efficiency, lower cost for small voltage transformations.
- Disadvantage: No electrical isolation between primary and secondary.
Instrument Transformers:
- Current Transformer (CT): Steps down current for measurement. Secondary is always short-circuited.
- Potential Transformer (PT): Steps down voltage for measurement. Secondary is open-circuited.

6. Electrical Engineering Materials

6.1 Insulating Materials (Dielectrics)

Materials that resist the flow of electric current.
- Properties: High dielectric strength (withstanding high voltage without breakdown), high resistivity, low dielectric loss (energy dissipated in dielectric).
- Applications: Cable insulation, capacitor dielectrics, transformer oil, circuit board substrates.
- Examples:
  - Solid: Mica, Porcelain, PVC, Rubber, Bakelite, Paper, Glass, Ceramics.
  - Liquid: Transformer oil, Silicone oil, Askarels (now largely banned due to toxicity).
  - Gaseous: Air, Nitrogen, Sulphur Hexafluoride (SF6).

6.2 Conducting Materials

Materials that allow electric current to flow easily.
- Properties: Low resistivity, high conductivity, good thermal conductivity, good mechanical strength and ductility (for wire