Problem Set 1

Problem

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

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Solution

Power is stored in resistors because of their linear behavior.

$Poc=Vo{c}^2/R$

Both Poc and Voc are giving so solve for R

$R=Vo{c}^2/Poc=5V/10W=2.5Ohms$ Answer

Apparent power relation to voltage and current is

$S^2=|Voc*Io{c}^{*}{|}^2$

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.

$S^2=P^2+Q^2$

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

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

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

$Q=Vo{c}^2/X$

$X=Vo{c}^2/Q=5V^2/224.8VAr=0.11H$