Question

How is the efficiency of a transformer calculated?

Answer 1

The efficiency of a transformer is a measure of how well it converts electrical power from the primary side (input) to the secondary side (output) without losing too much energy. It is calculated as the ratio of the useful power output to the power input.

The formula for calculating transformer efficiency is:

\[
\text{Efficiency} (\eta) = \left( \frac{\text{Power Output (P}_{\text{out}})}{\text{Power Input (P}_{\text{in}})} \right) \times 100
\]

Where:

1. \( \text{Power Output (P}_{\text{out}}) \) is the power delivered to the load (on the secondary side).
   

1. \( \text{Power Input (P}_{\text{in}}) \) is the power drawn from the supply (on the primary side).
   

In more detail:

1. Efficiency at Full Load:
   

   When the transformer is working at full load, the efficiency is typically calculated by considering the input power and the output power. The losses in the transformer, mainly copper losses (due to resistance in the windings) and core losses (due to the magnetic field), reduce the efficiency.

1. Formula considering losses:
   

   \[
   \eta = \frac{P_{\text{out}}}{P_{\text{in}}} = \frac{P_{\text{in}} - P_{\text{losses}}}{P_{\text{in}}} = 1 - \frac{P_{\text{losses}}}{P_{\text{in}}}
   \]
   Here, \( P_{\text{losses}} \) includes all losses (both copper and core losses).

Key Points:

1. If there are no losses, the transformer would have 100% efficiency, but in practice, there's always some loss.
   

1. The efficiency of a transformer is highest when it operates at or near full load.
   

1. For typical transformers, the efficiency can range from 95% to 99%.
   

To simplify, you can use the efficiency formula with the given values of power output and input to calculate how efficient the transformer is in transferring energy.