Problem Set 1

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


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


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.

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.


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