Problem Set 1

Problem

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

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Solution

Power is found only through resister

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

Both Poc and Voc are giving so solve for R

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

To calclate the core inductance we will use the formular for apparent power.

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

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

Subtituting in values and solving gives

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

Use the apparent power and the real power to find the reactive power

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

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

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

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