Problem Set 1

Problem

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

Solution

Power is found only through resister

$P o c = V o c^{2} / R$

Both Poc and Voc are giving so solve for R

$R = V o c^{2} / P o c = 5 V / 10 W = 2.5 O h m s < /! m a t h > T o c a l c l a t e t h e c o r e i n d u c t a n c e w e w i l l u s e t h e f o r m u l a r f o r a p p e a r e n t p o w e r . < m a t h > S^{2} = P^{2} + Q^{2}$

$S^{2} = | V o c * I o c^{*} |^{2}$

Subtituting in values aand solving gives $S^{2} = (5 V * 3 A)^{2} = 225 (V A)^{2}$

$Q = \sqrt{P^{2} - Q^{2}}$

$Z_{t h} = \frac{\frac{N_{1}}{N_{2}} e_{2}}{\frac{N_{2}}{N_{1}} i_{2}}$

Problem Set 1

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