Question

A transformer is connected to a 1000 V, 50 Hz supply. The total core loss is 1000 W of which 700 W are hysteresis loss and 300 W are eddy current loss. If the applied voltage is raised to 2000 V and the frequency to 100 Hz, then the new core loss is __________W.

• A. 2600

Answer 1

The correct option is A 2600
$\text{Hysteresis loss,}{P}_h\propto f{B}^x\propto f{\left(\frac{V}{f}\right)}^x$

$\frac{P_{h1}}{P_{h2}}=\frac{f_1}{f_2}{(\frac{V_1}{V_2}\times \frac{f_2}{f_1})}^x$

$\frac{700}{P_{h2}}=\frac{50}{100}{(\frac{1000}{2000}\times \frac{100}{50})}^x$

$P_{h2}=\frac{700\times 100}{50}=1400W$

$\text{Eddy current loss,}$

$P_e\propto B^2{f}^2\propto f^2{\left(\frac{V}{f}\right)}^2$

$\frac{P_{e1}}{P_{e2}}={\left(\frac{f_1}{f_2}\right)}^2{(\frac{V_1}{V_2}\times \frac{f_2}{f_1})}^2$

$\frac{300}{P_{e2}}={\left(\frac{50}{100}\right)}^2{\left(\frac{1000\times 100}{2000\times 50}\right)}^2$

$P_{e2}=1200W$

$\text{Total core loss,}{P}_c=P_{h2}+P_{e2}$

$\text{= 1400 + 1200}$

$\text{= 2600 W}$