Electromagnetic Induction

Voltage-and-turns ratio

For an ideal transformer, the voltage on each side of the iron core is proportional to the number of turns on that side:

Vp / Vs = Np / Ns

• where:
  • Vp = voltage across the primary coil (V)
  • Vs = voltage across the secondary coil (V)
  • Np = number of turns on the primary coil
  • Ns = number of turns on the secondary coil
• The equation can equally be written upside down (Vs / Vp = Ns / Np). Pick the form that puts the unknown on the top of a fraction so you have less rearranging to do
• The key fact: the ratio of voltages equals the ratio of turns

Conservation of energy

• An ideal transformer is 100 % efficient, with no energy lost as heat in the coils, the core, or eddy currents
• Real transformers reach about 99 % efficiency; the small loss appears as gentle warming of the iron core
• For an ideal transformer, the input electrical power equals the output electrical power:

Vp × Ip = Vs × Is

• where:
  • Ip = current in the primary coil (A)
  • Is = current in the secondary coil (A)
• This is just the statement P = V × I applied to both sides of the transformer
• A direct consequence: if the voltage is stepped up by some factor n, the current is stepped down by the same factor n, and vice versa