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## Q. 2.9

The total core loss of a specimen of silicon steel is found to be 1500 W at 50 Hz. Keeping the flux density constant the loss becomes 3000 W when the frequency is raised to 75 Hz. Calculate separately the hysteresis and eddy current loss at each of those frequencies.

## Verified Solution

From Eqs. (2.36)

$P_{h} =K_{h} fB^{n}_{m} W/ m^{3}$

and (2.37)

$P_{e} =K_{e} f^{2} B^{2} W/ m^{3}$

for constant flux density, total core loss can be expressed as

$P=Af+Bf^{2}$or P/ f=A+Bf
1500/ 50=A+50B    or    30=A+50B                             (i)
3000/ 75=A+75B    or    40=A+75B                              (ii)
Solving Eqs. (i) and (ii), we get A=10,B=2/ 5
Therefore $P=10f+2/ 5f^{2} =P_{h} +P_{e}$       (iii)
At 50 Hz $P_{h}=10\times 50=500$ W
$P_{e}=2/ 5\times 2500=1000$ W
At 75 Hz $P_{h}=10\times 75=750$W
$P_{e}=2/ 5\times \left(75\right) ^{2} =2250$ W