The output current corresponding to maximum efficiency of a transformer is:

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  1. \(\rm I_{2}=\sqrt{\frac{W_{i}}{R_{02}}}\)
  2. \(\rm I_{2}=\sqrt{\frac{W_{i}}{R_{01}}}\)
  3. \(\rm I_{2}=\sqrt{\frac{W_{c u}}{R_{02}}}\)
  4. \(\rm I_{2}=\sqrt{\frac{W_{c u}}{R_{01}}}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm I_{2}=\sqrt{\frac{W_{i}}{R_{02}}}\)
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Detailed Solution

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Concept:

The efficiency of a transformer is maximum when its iron loss (core loss) is equal to the copper loss.

Let iron loss be denoted by \( W \), and copper loss by \( I_2^2 R \), where:

  • \( I_2 \) is the output current
  • \( R \) is the equivalent resistance referred to the secondary side

Condition for maximum efficiency:

\( I_2^2 R = W \)

Solving for \( I_2 \):

\( I_2 = \sqrt{\frac{W}{R}} \)

 

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