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GATE IN 2021 Official Paper

Option 2 : 50.6%

**Concept:**

For maximum efficiency to occur in a transformer

Ironlosses = copperlosses

W_{i} = W_{cu}

W_{i} = x^{2} × W_{cuFL}

\(x = \sqrt {\frac{{{W_i}}}{{{W_{cuFL}}}}} \)

Here,

x = percentage of loading at maximum efficiency

W_{cuFL} = full load copper losses

**Calculation:**

Given:

R_{primary} = 0.5 Ω_{,} I_{rated }= 25 A, W_{i} = 80 W, η_{max} = 98%

W_{cuFL }= I^{2}_{rated} × R_{primary }= 25^{2} × 0.5 = 312.5 W

\(x = \sqrt \frac{{80}}{{312.5}}\)

x = 0.505 = **50.5%**