Question

A 230V, 2.5 kVA single phase transformer has an
iron loss of 100 watt at 40 Hz and 70 Watt at 30
Hz. Find the
hysteresis and eddy current losses at
50 Hz​

Answer 1

The hysteresis losses is 90 Watt

The eddy current losses is 42.5 Watt

Explanation:

Given:

A 230 V, 2.5 KVA single phase transformer has an iron loss of 100 watt at 40 Hz and 70 watt at 30 Hz

To find out:

The hysteresis and eddy current losses at 50 Hz

Solution:

Hysteresis loss is proportional to frequency f and eddy loss is proportional to square of the frequency

Thus,

Hysteresis loss

$W_h=K_hf$

And

Eddy loss

$W_e=K_ef^2$

Total iron loss

$W=W_h+W_e$

$\implies W=K_hf+K_ef^2$

When $W=100$ Watt, $f=40$ Hz

Thus,

$100=K_h\times 40+K_e\times 40^2$

$\implies K_h+40K_e=2.5$                      (1)

When $W=70$ Watt, $f=30$ Hz

Thus,

$70=K_h\times 30+K_e\times 30^2$

$\implies 3K_h+90K_e=7$                         (2)

Multiplying equation (1) by 3 and subtracting eq (2) from eq (1)

$30K_e=7.5-7$

$\imples K_e=0.5/30=0.017$

Putting the value of $K_e$ in eq (1)

$K_h+40\times 0.017=2.5$

$\implies K_h=1.8$

Thus,

At 50 Hz

$W_h=1.8\times 50=90$ Watt

$W_e=0.017\times 50^2$

$\implies W_e=42.5$ Watt

Hope this answer is helpful.

Know More:

Q: In a transformer, the core loss is found to be 52 watts at 40 Hz and 90 Watts at 60 Hz; both losses being measured at the same peak flux density. Compute the hysteresis and eddy current losses at 50 Hz.

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