7.3.6 Transformer Equations

• What is the primary purpose of transformers in electrical systems?

  To change the voltage level of alternating current (AC).
• Why is understanding transformer equations important?

  It is crucial for solving problems related to voltage, current, and power in AC circuits.
• What is the basic principle of a transformer?

  • Changes voltage level of AC in a circuit
  • Transfers electrical power through electromagnetic induction
  • Consists of two or more coils wrapped around a common core
• How does a transformer work?

  AC flowing through the primary coil creates a changing magnetic field that induces a voltage in the secondary coil.
• What is the equation that relates the primary and secondary voltages of a transformer?


  \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\)
• What do the variables \(V_p\), \(V_s\), \(N_p\), and \(N_s\) represent in the voltage relationship equation?

  \(V_p\) is primary voltage, \(V_s\) is secondary voltage, \(N_p\) is the number of turns in the primary coil, and \(N_s\) is the number of turns in the secondary coil.
• What happens to the voltage when the number of turns in the secondary coil is greater than in the primary coil?

  The voltage is stepped up.
• What is the relationship between primary and secondary currents in a transformer?

  The primary and secondary currents are inversely proportional to the turns ratio.
• What is the equation that relates the primary and secondary currents of a transformer?


  \(\frac{I_p}{I_s} = \frac{N_s}{N_p}\)
• What does it mean if the voltage is stepped up in a transformer?

  The current in the secondary coil will be lower than in the primary coil.
• What is the power relationship in an ideal transformer?

  The power input to the primary coil equals the power output from the secondary coil.
• What is the equation for power in a transformer?


  \(V_p \times I_p = V_s \times I_s\)
• What does the efficiency of a transformer measure?

  It measures the effectiveness of power transfer from primary to secondary.
• What is the equation for the efficiency of a transformer?


  \(\eta = \frac{P_s}{P_p} \times 100\%\)
• What are the key equations related to transformers?

  • Voltage Relationship: \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\)
  • Current Relationship: \(\frac{I_p}{I_s} = \frac{N_s}{N_p}\)
  • Power Relationship: \(V_p \times I_p = V_s \times I_s\)
• What are some applications of transformers?

  • Power transmission
  • Voltage regulation
  • Adaptation of voltage levels in various electrical devices
• What is the summary of transformer principles?

  • Transformers change AC voltage levels through electromagnetic induction.
  • Efficiency measures the effectiveness of power transfer.
  • Understanding these principles aids in designing and analyzing transformer-based systems.