Problem Set 1: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(5 intermediate revisions by the same user not shown)
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>
Line 15: Line 15:
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>
<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.
Subtituting in values and solving gives


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


Use the apparent power and the real power to find the reactive power
Apparent power S is complex. It has a real part P, real power, and an imaginary part Q, reactive power.


<math>Q=\sqrt{S^{2}-P^{2}}= \sqrt{225^{2}-10^{2}}= 224.8VAr\!</math>
<math>S=P+iQ\!</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.
Finally


<math>Q=Voc^{2}/X\!</math>
<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.
Solve for the inductance


<math>Q=Voc^{2}/X\!</math>
<math>Q=Voc^{2}/X\!</math>


<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'''''

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

Retrieved from "http:///class-wiki/index.php?title=Problem_Set_1&oldid=8938"