Problem Set 1: Difference between revisions
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'''PROBLEM''' |
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Find the core inductance and resistance of a transformer using measurements Voc=5V, Ioc=3A, and Poc =10W. |
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1. A solenoid transformer has 3V and .5 A on its primary winding. The leakage flux of this transformer is 2Wb. Find the amount of flux created and by primary winding, the flux created by the secondary winding, and the efficiency of the transformer. |
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2. An non-ideal 2-phase transformer core has Rc1= 2 Ohms and Lw1= 5 micro Henrys. The average flux created when the transformer is connected to an open circuit is 5Wb. Find Rc2 and Lw2. |
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'''SOLUTION''' |
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3. The flux created by a transformer’s primary winding is 3Wb and the flux from the secondary is 1WB. Find the leakage flux. |
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Power is stored in resistors because of their linear behavior. |
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4. Find the amount of energy lost in a magnet by using Green’s theorem to approximate the area of its characteristic BH curve shown. |
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<math>Poc= Voc^{2}/R\!</math> |
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5. Derive the power equation for an ideal three phase transformer. Interms of |
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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''''' |
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Apparent power relation to voltage and current is |
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<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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<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 can be expressed using the equation of a circle. |
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<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> |
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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> |
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<math>X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H \!</math> '''''Answer''''' |
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'''Solutions''' |
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Latest revision as of 23:43, 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
