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 $120\sqrt{2}\mathrm{\angle }0$° applied to it at a frequency of 60Hz.
• $\frac{N_1}{N_2}=3$
• The combined load on winding 2 is ${Z}_L=(5+j3)\mathrm{\Omega }$

Solution

${e}_1(t)=V_1\cos (\omega t)$

$\omega =2\pi f$, so $\omega =120\pi$

Therefore, ${e}_1(t)=V_1\cos (120\pi t)$

Now the Thevenin equivalent impedance, ${Z}_{th}$, is found through the following steps:

$Z_{th}=\frac{e_1}{i_1}$

$=\frac{\frac{N_1}{N_2}{e}_2}{\frac{N_2}{N_1}{i}_2}$

$=(\frac{N_1}{N_2}{)}^2{R}_L$

Now, substituting:

${Z}_{th}=3^2(5+j3)$

$=(45+j27)\mathrm{\Omega }$

Since $i_1=\frac{e_1}{R_{th}}$,

$i_1=\frac{120\sqrt{2}}{45+j27}$

Contributors

Christopher Garrison Lau I

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John Hawkins