Transformer Theory and Equations

Overview

• Transformers are used to change the potential difference in an electricity supply.
• Step Up Transformers: Increase potential difference (more turns on secondary coil).
• Step Down Transformers: Decrease potential difference (fewer turns on secondary coil).

Key Equations

• Two equations are used to relate potential difference and current to the number of turns on each coil.
• Variables:
  • V: Potential difference
  • N: Number of turns on the coil
  • I: Current
  • Subscripts 'p' and 's' refer to the primary and secondary coils respectively.

Example Problem 1: Calculating Output Potential Difference

• Given:
  • Primary turns (Nₚ): 18
  • Secondary turns (Nₛ): 54
  • Input potential difference (Vₚ): 45V
  • Looking for output potential difference (Vₛ)
• Equation Used:
  • ( \frac{Vₚ}{Vₛ} = \frac{Nₚ}{Nₛ} )
• Calculation Steps:
  1. Substitute known values: ( \frac{45}{Vₛ} = \frac{18}{54} )
  2. Simplify ( \frac{18}{54} = 0.33 )
  3. Rearrange to solve for Vₛ: ( Vₛ = 45 / 0.33 )
  4. Result: Vₛ = 135V

Example Problem 2: Calculating Output Current

• Given:
  • Input current (Iₚ): 12A
  • Looking for output current (Iₛ)
• Equation Used:
  • ( Vₚ \cdot Iₚ = Vₛ \cdot Iₛ )
• Calculation Steps:
  1. Substitute known values: ( 45 \times 12 = 135 \times Iₛ )
  2. Solve for Iₛ: ( Iₛ = \frac{45 \times 12}{135} )
  3. Result: Iₛ = 4A

Conclusion

• Covered how to use the two main equations for transformers.
• Examples provided for calculating output potential difference and output current.
• Essential practice for understanding transformer functionality and calculations.