An Ideal Transformer Example: Difference between revisions

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Since <math>{i_{1}}=\frac{e_{1}}{R_{th}}</math>,
Since <math>{i_{1}}=\frac{e_{1}}{R_{th}}</math>,


<math>{i_{1}}=\frac{120sqrt{2}}{45+j27}</math>
<math>{i_{1}}=\frac{120\sqrt{2}}{45+j27}</math>

Revision as of 14:08, 17 January 2010

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

  • Winding 1 has a sinusoidal voltage of 12020° applied to it at a frequency of 60Hz.
  • N1N2=3
  • The combined load on winding 2 is ZL=(5+j3)Ω

Solution

e1(t)=V1cos(ωt)

ω=2πf, so ω=120π

Therefore, e1(t)=V1cos(120πt)

Now the Thevenin equivalent impedance, Zth, is found through the following steps:

Zth=e1i1

=N1N2e2N2N1i2

=(N1N2)2RL

Now, substituting:

Zth=32(5+j3)

=(45+j27)Ω

Since i1=e1Rth,

i1=120245+j27