Nicholas.Christman at 01:05, 27 January 2010

2010-01-27T01:05:06Z

← Older revision		Revision as of 18:05, 26 January 2010
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	~~==Transformer Example==~~

	'''[[Kevin Starkey EMEC]], [[Nick Christman]], [[Aric Vyhmeister]]'''		'''[[Kevin Starkey EMEC]], [[Nick Christman]], [[Aric Vyhmeister]]'''

Nicholas.Christman: New page: ==Transformer Example== '''Kevin Starkey EMEC, Nick Christman, Aric Vyhmeister''' '''Problem:''' A step down transformer has a winding of $N_1 = 10 \text{ tur...$

2010-01-27T01:04:34Z

New page: ==Transformer Example== '''Kevin Starkey EMEC, Nick Christman, Aric Vyhmeister''' <u>'''Problem:'''</u> A step down transformer has a winding of <math> N_1 = 10 \text{ tur...

New page

==Transformer Example==

'''[[Kevin Starkey EMEC]], [[Nick Christman]], [[Aric Vyhmeister]]'''

<u>'''Problem:'''</u>

A step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. (a) If the input voltage is 1200V, what is the resulting output voltage? (b) If the input and output currents are <math>5A \mbox{ and } 20A</math>, respectively, what is the current loss due to the leakage inductance, <math>i_{m}(t)</math>.

<center>
{|
|[[Image:IdealTransformer1-nka.jpg|thumb|center|upright=2|Figure 1: Model for an ideal transformer.]]
|[[Image:IdealTransformer2-nka.jpg|thumb|center|upright=2|Figure 2: Magnetic circuit of an ideal transformer.]]
|}
</center>

<u>'''Solution:'''</u>

a) By modifying equation 5-39 (Mohan 5-22) we can obtain an equation for the output voltage. That is,
<br/>

<div style="text-align:center">
<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 </math>.
</div>

<br/>

With the information provided we can now determine the output voltage:
<br/>

<div style="text-align:center">
<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V </math>
</div>
<br/>

b) From the figure above, we need to find the true value of current (i.e. the current that is not lost by leakage inductance). To accomplish this we will use equation 5-40 (Mohan 5-23) to obtain the value of <math>i_{1}^{'}</math>. That is,
<br/>

<div style="text-align:center">
<math>i_{1}^{'} = \left( \frac{N_2}{N_1} \right) i_{2} = \left( \frac{2}{10} \right) 20A = 4A</math>.
</div>

Now from equation 5-42 (Mohan 5-23) we can obtain the current loss due to the leakage inductance, which is
<br/>

<div style="text-align:center">
<math>i_{m} = i_{1} - i_{1}^{'} = 5A - 4A = 1A</math>.
</div>

Therefore, the current loss in our transformer is <math>1A</math>, which means this specific transformer is very "leaky."

Transformer Example Problem - Revision history

Nicholas.Christman at 01:05, 27 January 2010

Nicholas.Christman: New page: ==Transformer Example== '''Kevin Starkey EMEC, Nick Christman, Aric Vyhmeister''' '''Problem:''' A step down transformer has a winding of N_1 = 10 \text{ tur...

Nicholas.Christman: New page: ==Transformer Example== '''Kevin Starkey EMEC, Nick Christman, Aric Vyhmeister''' '''Problem:''' A step down transformer has a winding of $N_1 = 10 \text{ tur...$