An Ideal Transformer Example: Difference between revisions

Revision as of 13:45, 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 $120 \sqrt{2} ∠ 0$ ° 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:

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

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

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

Revision as of 13:43, 17 January 2010 view source Cdxskier (talk \| contribs) 319 edits →Solution ← Older edit		Revision as of 13:45, 17 January 2010 view source Cdxskier (talk \| contribs) 319 edits →Solution Newer edit →
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	<math>=\frac{\frac{N_{1}}{N_{2}}{e_{2}}}{\frac{N_{2}}{N_{1}}{i_{2}}}</math>		<math>=\frac{\frac{N_{1}}{N_{2}}{e_{2}}}{\frac{N_{2}}{N_{1}}{i_{2}}}</math>

	<math>=(\frac{{N_{1}}{N_{2}})^2{R_{L}}</math>		<math>=(\frac{N_{1}}{N_{2}})^2{R_{L}}</math>