Problem Set 1: Difference between revisions
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'''PROBLEM''' |
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'''SOLUTION''' |
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Power is stored in resistors because of their linear behavior. |
Power is stored in resistors because of their linear behavior. |
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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> Answer |
<math>R=Voc^{2}/Poc=5V/10W=2.5 Ohms\!</math> ''''' Answer''''' |
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Apparent power relation to voltage and current is |
Apparent power relation to voltage and current is |
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<math>S=P+iQ\!</math> |
<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 |
Apparent power in the imaginary and real coordinate system is the hypotenuse of real and reactive power and can be expressed using the equation of a circle. |
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<math>S^{2}=P^{2}+Q^{2}\!</math> |
<math>S^{2}=P^{2}+Q^{2}\!</math> |
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Solve the above equation for reactive power using the values of apparent and real 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> |
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Reactive power is stored in non-linear impedance represented as X. In this case X is inductance. |
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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<math>X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H \!</math> |
<math>X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H \!</math> '''''Answer''''' |
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Latest revision as of 22:43, 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 can be expressed using the equation of a circle.
Solve the above equation for reactive power using the values of apparent and real power.
Reactive power is stored in non-linear impedance represented as X. In this case X is inductance.
Answer
