The no-load current of a $$ 8880 / 400 \mathrm{~V} $$ single-phase transformer is 10 A at a power factor of 0,1 . The primary winding has 40 turns and the supply frequency is 50 Hz . Calculate: 4.2 .1 The maximum value of the flux in the core 4.2 .2 The value of the magnetizing current

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**Step 1. Maximum Value of the Flux in the Core**

For a transformer, the relationship between the RMS applied voltage, the number of turns $$ N $$, the supply frequency $$ f $$, and the maximum flux $$ \Phi_{\max} $$ is given by

$$
E_{\mathrm{rms}} = 4.44\, f\, N\, \Phi_{\max}.
$$

Solving for $$ \Phi_{\max} $$ we have

$$
\Phi_{\max} = \frac{E_{\mathrm{rms}}}{4.44\, f\, N}.
$$

Using the primary voltage $$ E_{\mathrm{rms}} = 8880\,\mathrm{V} $$, $$ f = 50\,\mathrm{Hz} $$, and $$ N = 40 $$ turns,

$$
4.44\, f\, N = 4.44 \times 50 \times 40 = 4.44 \times 2000 = 8880.
$$

Thus,

$$
\Phi_{\max} = \frac{8880}{8880} = 1\,\mathrm{Wb}.
$$

**Step 2. Value of the Magnetizing Current**

The no-load current is $$ I_0 = 10\,\mathrm{A} $$ with a power factor of 0.1. Since the power factor $$ \cos \phi = 0.1 $$, the phase angle $$ \phi $$ is

$$
\phi = \cos^{-1}(0.1) \approx 84.3^\circ.
$$

In a transformer under no-load conditions, the current can be decomposed into:

- A magnetizing (reactive) component $$ I_m $$ (which is $$ I_0 \sin \phi $$),
- A core loss (resistive) component $$ I_c $$ (which is $$ I_0 \cos \phi $$).

The magnetizing current is given by

$$
I_m = I_0 \sin \phi.
$$

Calculating $$ I_m $$:

$$
I_m = 10\,\mathrm{A} \times \sin(84.3^\circ) \approx 10\,\mathrm{A} \times 0.995 \approx 9.95\,\mathrm{A}.
$$

Thus, the magnetizing current is approximately

$$
I_m \approx 10\,\mathrm{A}.
$$

**Final Answers:**

4.2.1 The maximum value of the flux in the core is $$ 1\,\mathrm{Wb} $$.

4.2.2 The value of the magnetizing current is approximately $$ 10\,\mathrm{A} $$.
The maximum flux in the core is 1 Wb, and the magnetizing current is approximately 10 A.

The no-load current of a single-phase transformer is 10 A at a
power factor of 0,1 . The primary winding has 40 turns and the supply frequency
is 50 Hz .
Calculate:
4.2 .1 The maximum value of the flux in the core
4.2 .2 The value of the magnetizing current

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The no-load current of a single-phase transformer is 10 A at a power factor of 0,1 . The primary winding has 40 turns and the supply frequency is 50 Hz . Calculate: 4.2 .1 The maximum value of the flux in the core 4.2 .2 The value of the magnetizing current