At 400 V and 50 Hz, the total core loss in a transformer is 2400 W. When the transformer is supplied at 200 V, 25 Hz, the core loss is 800 W. Find the hysteresis loss at 400 V, 50 Hz.

Correct option is D

​$$\text{Given,}\\V_1 = 400 \, \text{V}, \, f_1 = 50 \, \text{Hz}, \, V_2 = 200 \, \text{V}, \, f_2 = 25 \, \text{Hz}\\\quad \frac{V_1}{f_1} = \frac{V_2}{f_2} = \frac{400}{50} = \frac{200}{25} = 8\\\text{Hence, (V/f) ratio is constant,}\\\text{At frequency, 50 Hz,}\\\quad P_i = 2400 \, \text{W} = P_h + P_e = af + bf^2\\\quad \Rightarrow \frac{2400}{f} = a + bf\\\quad \Rightarrow a + 50b = 48 \, \text{W} \quad \cdots \, (a)\\\text{At frequency, 25 Hz,}\\\quad P_i = 800 \, \text{W} = P_h + P_e = af + bf^2\\\quad \Rightarrow \frac{800}{f} = a + bf\\\quad \Rightarrow a + 25b = 32 \, \text{W} \quad \cdots \, (b)\\\text{Calculating equations (a) and (b),}\\\quad a = 16 \quad \text{and} \quad b = 0.64\\\text{Now, at frequency 50 Hz and 400 V,}\\\quad \text{Hysteresis loss,} \, P_h = af = (16 \times 50) \, \text{W} = 800 \, \text{W}\\$$​​