# Problem Set 1

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

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