Problem Set 1: Difference between revisions

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'''Problem'''
'''PROBLEM'''


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Find the core inductance and resitence of a transformer using measurmnets Voc=5V, Ioc=3A, and Poc =10W.
Find the core inductance and resistance of a transformer using measurements Voc=5V, Ioc=3A, and Poc =10W.


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'''Solution'''
'''SOLUTION'''


Power is stored in resistors because of their linear behavior.
Power is found only through resister


<math>Poc= Voc^{2}/R</math>
<math>Poc= Voc^{2}/R\!</math>


Both Poc and Voc are giving so solve for R
Both Poc and Voc are giving so solve for R


<math>R=Voc^{2}/Poc=5V/10W=2.5 Ohms</math>
<math>R=Voc^{2}/Poc=5V/10W=2.5 Ohms\!</math> ''''' Answer'''''


Apparent power relation to voltage and current is
To calclate the core inductance we will use the formular for apparent power.


<math>S^{2}=P^{2}+Q^{2}</math>
<math>S^{2}=|Voc*Ioc^{*}|^{2}\!</math>


The magnitude for current and voltage are given in the problem statement. Subtitute in known values and solve.
⚫
<math>S^{2}=|Voc*Ioc^{*}|^{2}</math>


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<math>S^{2}=(5V*3A)^{2}=225(VA)^{2}\!</math>
Subtituting in values and solving gives


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^{2}=(5V*3A)^{2}=225(VA)^{2}</math>


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<math>S=P+iQ\!</math>
Use the apparent power and the real power to find the 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.
⚫
<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr</math>


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<math>S^{2}=P^{2}+Q^{2}\!</math>
Finally


Solve the above equation for reactive power using the values of apparent and real power.
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<math>Q=Voc^{2}/X</math>


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<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr\!</math>
Solve for the inductance


Reactive power is stored in non-linear impedance represented as X. In this case X is inductance.
<math>Q=Voc^{2}/X</math>


<math>X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H </math>
<math>Q=Voc^{2}/X\!</math>

<math>X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H \!</math> '''''Answer'''''

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

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