An Ideal Transformer Example

Consider a simple, transformer with two windings. Find the current provided by the voltage source.

Winding 1 has a sinusoidal voltage of $120 \sqrt{2} ∠ 0$ ° applied to it at a frequency of 60Hz.
$\frac{N_{1}}{N_{2}} = 3$
The combined load on winding 2 is $Z_{L} = (5 + j 3) Ω$

$e_{1} (t) = V_{1} \cos (ω t)$

$ω = 2 π f$ , so $ω = 120 π$

Therefore, $e_{1} (t) = V_{1} \cos (120 π t)$

Now the Thevenin equivalent impedance, $Z_{t h}$ , is found through the following steps:

$Z_{t h} = \frac{e_{1}}{i_{1}}$

$= \frac{\frac{N_{1}}{N_{2}} e_{2}}{\frac{N_{2}}{N_{1}} i_{2}}$

$= (\frac{N_{1}}{N_{2}})^{2} R_{L}$

Now, substituting:

$Z_{t h} = 3^{2} (5 + j 3)$

$= (45 + j 27) Ω$

Since $i_{1} = \frac{e_{1}}{R_{t h}}$ ,

$i_{1} = \frac{120 \sqrt{2}}{45 + j 27}$

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