Problem Set 1: Difference between revisions
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Find the core inductance and |
Find the core inductance and resistance of a transformer using measurements Voc=5V, Ioc=3A, and Poc =10W. |
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'''Solution''' |
'''Solution''' |
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Power is stored in resistors because of their linear behavior. |
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Power is found only through resister |
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<math>Poc= Voc^{2}/R\!</math> |
<math>Poc= Voc^{2}/R\!</math> |
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Both Poc and Voc are giving so solve for R |
Both Poc and Voc are giving so solve for R |
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<math>R=Voc^{2}/Poc=5V/10W=2.5 Ohms\!</math> |
<math>R=Voc^{2}/Poc=5V/10W=2.5 Ohms\!</math> Answer |
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Apparent power relation to voltage and current is |
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To calclate the core inductance we will use the formular for apparent power. |
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<math>S^{2}=|Voc*Ioc^{*}|^{2}\!</math> |
<math>S^{2}=|Voc*Ioc^{*}|^{2}\!</math> |
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The magnitude for current and voltage are given in the problem statement. Subtitute in known values and solve. |
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Subtituting in values and solving gives |
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<math>S^{2}=(5V*3A)^{2}=225(VA)^{2}\!</math> |
<math>S^{2}=(5V*3A)^{2}=225(VA)^{2}\!</math> |
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Apparent power S is complex. It has a real part P, real power, and an imaginary part Q, reactive power. |
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<math>S=P+iQ\!</math> |
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Apparent power in the imaginary and real coordinate system is the hypotenuse of real and reactive power and are related using the equation of a circle. |
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Use the apparent power and the real power to find the reactive power |
Use the apparent power and the real power to find the reactive power |
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<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr\!</math> |
<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr\!</math> Answer |
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Reactive power is stored in non-linear |
Reactive power is stored in non-linear impedance represented as X. In this case X is inductance. |
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<math>Q=Voc^{2}/X\!</math> |
<math>Q=Voc^{2}/X\!</math> |
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Revision as of 22:34, 8 February 2010
Problem
Find the core inductance and resistance of a transformer using measurements Voc=5V, Ioc=3A, and Poc =10W.
Solution
Power is stored in resistors because of their linear behavior.
Both Poc and Voc are giving so solve for R
Answer
Apparent power relation to voltage and current is
The magnitude for current and voltage are given in the problem statement. Subtitute in known values and solve.
Apparent power S is complex. It has a real part P, real power, and an imaginary part Q, reactive power.
Apparent power in the imaginary and real coordinate system is the hypotenuse of real and reactive power and are related using the equation of a circle.
Use the apparent power and the real power to find the reactive power
Answer
Reactive power is stored in non-linear impedance represented as X. In this case X is inductance.
