Example Problems with Transformers - Revision history

Nicholas.Christman at 01:03, 27 January 2010

2010-01-27T01:03:17Z

← Older revision		Revision as of 18:03, 26 January 2010
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	==Transformer Example==		==Transformer Example==

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

Nicholas.Christman at 01:02, 27 January 2010

2010-01-27T01:02:24Z

← Older revision		Revision as of 18:02, 26 January 2010
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	<u>'''Problem:'''</u>		<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>.		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>		<center>
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	<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V </math>		<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V </math>
	</div>		</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,		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,

Nicholas.Christman at 01:01, 27 January 2010

2010-01-27T01:01:08Z

← Older revision		Revision as of 18:01, 26 January 2010
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	==~~Problems 1-3~~==		==Transformer Example==

	'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''		'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''


	'''Problem ~~1.''' An '~~'~~ideal~~'' ~~step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2~~ </~~math~~> ~~turns. If the input voltage is 1200V, what is the resulting output voltage?~~		<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>		<center>
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	'''Solution'''		<u>'''Solution:'''</u>

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

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	<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V </math>		<math> e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V </math>
	</div>		</div>

			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."

Nicholas.Christman at 00:37, 27 January 2010

2010-01-27T00:37:08Z

← Older revision		Revision as of 17:37, 26 January 2010
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	'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?		'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?


			<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>


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

	<br/>		<br/>

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

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

	~~<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>~~

Nicholas.Christman: /* Problems 1-3 */

2010-01-27T00:34:39Z

Problems 1-3

← Older revision		Revision as of 17:34, 26 January 2010
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	'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?		'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?

	'''Solution''' ~~Using the equation <math> e_2 = \frac{N_2}{N_1}e_1 </math> we get <br>~~		'''Solution'''

	<math> e_2 = \frac{2}{10}1200 = 240V </math>		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 = \frac{N_2}{N_1}e_1 </math>.
			</div>

			<br/>

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

			<div style="text-align:center">
			<math> e_2 = \frac{2}{10}1200 = 240V </math>
			</div>

	<center>		<center>

Nicholas.Christman at 15:45, 20 January 2010

2010-01-20T15:45:54Z

← Older revision		Revision as of 08:45, 20 January 2010
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	'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''		'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''


	'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?		'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?
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	<math> e_2 = \frac{2}{10}1200 = 240V </math>		<math> e_2 = \frac{2}{10}1200 = 240V </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>

Kevin.Starkey at 04:08, 18 January 2010

2010-01-18T04:08:22Z

← Older revision		Revision as of 21:08, 17 January 2010
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	'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?		'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?

	'''Solution''' Using the equation <math> e_2 = \frac{N_2}{N_1}e_1 </math> we get		'''Solution''' Using the equation <math> e_2 = \frac{N_2}{N_1}e_1 </math> we get <br>

	<math> e_2 = \frac{2}{10}1200 = 240V </math>		<math> e_2 = \frac{2}{10}1200 = 240V </math>

Kevin.Starkey at 04:07, 18 January 2010

2010-01-18T04:07:23Z

← Older revision		Revision as of 21:07, 17 January 2010
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	'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''		'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''

			'''Problem 1.''' An ''ideal'' step down transformer has a winding of <math> N_1 = 10 \text{ turns and } N_2 = 2 </math> turns. If the input voltage is 1200V, what is the resulting output voltage?

			'''Solution''' Using the equation <math> e_2 = \frac{N_2}{N_1}e_1 </math> we get
			<math> e_2 = \frac{2}{10}1200 = 240V </math>

Kevin.Starkey at 03:32, 18 January 2010

2010-01-18T03:32:31Z

← Older revision		Revision as of 20:32, 17 January 2010
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	''Problems 1-3''		==Problems 1-3==

	==Kevin Starkey, Nick Christman, Aric Vyhmeister==		'''Kevin Starkey, Nick Christman, Aric Vyhmeister'''

Kevin.Starkey: New page: ''Problems 1-3'' ==Kevin Starkey, Nick Christman, Aric Vyhmeister==

2010-01-18T03:26:16Z

New page: ''Problems 1-3'' ==Kevin Starkey, Nick Christman, Aric Vyhmeister==

New page

''Problems 1-3''

==Kevin Starkey, Nick Christman, Aric Vyhmeister==