Question

At 400 V and 50 Hz the total core loss of a transformer was found to be 3200W. When the transformer is supplied at 200V and 25 Hz the core loss is 1000W. The hysteresis and eddy current loss at 400V and 50 Hz will be respectively

• A. 1200 W , 2000 W
• B. 800 W, 2400 W
• C. 2400 W , 800 W
• D. 1600 W , 1600 W

Answer 1

The correct option is B 800 W, 2400 W

$\text{For first case}\frac{V_1}{f_1}=\frac{400}{50}=8$

$\text{For second case}\frac{V_2}{f_2}=\frac{200}{25}=8$

$\text{Since}\frac{V_1}{f_1}=\frac{V_2}{f_2}=8\text{; the flux density}{B}_m\text{remains constant}$

$\text{Now, Hysteresis loss,}$ $P_h=K_{1}f$

$\text{and Eddy current loss ;}{P}_e=K_2{f}^2$

$\text{Then, Iron loss}{P}_i=K_{1}f+K_2{f}^2$

$or,\frac{P_i}{f}=K_2+K_{2}f$ ...(i)

$\text{Now, from}{1}^{st}case$
$\frac{3200}{50}=K_1+K_2\times 50$ ...(ii)

$\text{From}{2}^{nd}\text{case}$
$\frac{1000}{25}=K_1+25K_2$ ...(iii)

$\text{From (ii) and (iii), we get}$
$K_1=16$
$and{K}_2=\frac{24}{25}$

$\text{Hysteresis loss,}{P}_h=16\times 50=800W$
$\text{and, eddy current loss,}{P}_e=\frac{24}{25}\times 2500=2400W$