Problem Set 1: Difference between revisions

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.

$Poc=Voc^{2}/R\!$

Both Poc and Voc are giving so solve for R

$R=Voc^{2}/Poc=5V/10W=2.5Ohms\!$ Answer

Apparent power relation to voltage and current is

$S^{2}=|Voc*Ioc^{*}|^{2}\!$

The magnitude for current and voltage are given in the problem statement. Subtitute in known values and solve.

$S^{2}=(5V*3A)^{2}=225(VA)^{2}\!$

Apparent power S is complex. It has a real part P, real power, and an imaginary part Q, reactive power.

$S=P+iQ\!$

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.

$S^{2}=P^{2}+Q^{2}\!$

Solve the above equation for reactive power using the values of apparent and real power.

$Q={\sqrt {S^{2}-P^{2}}}={\sqrt {225^{2}-10^{2}}}=224.8VAr\!$

Reactive power is stored in non-linear impedance represented as X. In this case X is inductance.

$Q=Voc^{2}/X\!$

$X=Voc^{2}/Q=5V^{2}/224.8VAr=0.11H\!$ Answer

@@ Line 1: / Line 1: @@
-'''Problem'''
+'''PROBLEM'''
 ----
-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.
 ----
-'''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
-<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 appearent 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>
+<math>S^{2}=(5V*3A)^{2}=225(VA)^{2}\!</math>
-Subtituting in values  aand solving gives
-<math>S^{2}=(5V*3A)^{2}=225(VA)^{2}</math>
+Apparent power S is complex. It has a real part P, real power, and an imaginary part Q, reactive power.
-<math>Q=\sqrt{P^{2}-Q^{2}}</math>
+<math>S=P+iQ\!</math>
-<math>{Z_{th}}=\frac{\frac{N_{1}}{N_{2}}{e_{2}}}{\frac{N_{2}}{N_{1}}{i_{2}}}</math>
+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>S^{2}=P^{2}+Q^{2}\!</math>
+Solve the above equation for reactive power using the values of apparent and real power.
+<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr\!</math>
+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> '''''Answer'''''

Problem Set 1: Difference between revisions

Latest revision as of 22:43, 8 February 2010

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