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Introduction to Transformers

  • Transformers serve to change or transform the voltage in an electrical circuit.

Types of Transformers

  • Step-Up Transformer:
    • Increases the voltage and decreases the amperage.
  • Step-Down Transformer:
    • Decreases the voltage and increases the amperage.
  • Both types operate based on the number of turns in the transformer.

Formula for Calculating Voltage Change

  • The core formula for voltage change in a transformer is:
    • \frac{Vs}{Vp} = \frac{Ns}{Np}
  • Where:
    • $V_s$ = Secondary voltage
    • $V_p$ = Primary voltage
    • $N_s$ = Number of turns on the secondary side
    • $N_p$ = Number of turns on the primary side

Representation of Variables on a Diagram

  • $V_p$ = Voltage on the primary side.
  • $N_p$ = Number of turns on the primary side.
  • $N_s$ = Number of turns on the secondary side.
  • $V_s$ = Voltage on the secondary side.

Importance of the Turns Ratio

  • The fraction \frac{Ns}{Np} is known as the turns ratio.
  • It has practical significance in determining how the voltage changes based on the turns in the transformer.

Rearranging the Equation

  • The formula can be rearranged to directly solve for the secondary voltage:
    • Vs = Vp \cdot \frac{Ns}{Np}

Sample Problem: Turns Ratio Calculation

  • Problem: What is the turns ratio for a transformer having 40 primary turns and 4,000 secondary turns?
  • Solution:
    • Turns ratio = \frac{Ns}{Np} = \frac{4000}{40} = 100:1

Practice Problem #1: Voltage Calculation

  • Problem: What is the voltage produced by a transformer receiving 220 volts if the primary side has 100 turns and the secondary side has 10,000 turns?
  • Analysis:
    • More secondary turns indicate this is a step-up transformer.
  • Calculation: Using modified formula:
    • V_s = 220 \cdot \frac{10,000}{100} = 220 \cdot 100 = 22,000 \text{ volts}

Practice Problem #2: Voltage Calculation

  • Problem: What is the voltage produced by a transformer receiving 220 volts if the primary side has 10 turns and the secondary side has 400 turns?
  • Calculation: Using modified formula:
    • V_s = 220 \cdot \frac{400}{10} = 220 \cdot 40 = 8,800 \text{ volts}