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 {\displaystyle Poc=Voc^{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 {\displaystyle R=Voc^{2}/Poc=5V/10W=2.5Ohms</!math>Tocalclatethecoreinductancewewillusetheformularforappearentpower.<math>S^{2}=P^{2}+Q^{2}}
S 2 = | V o c ∗ I o c ∗ | 2 {\displaystyle S^{2}=|Voc*Ioc^{*}|^{2}}
Subtituting in values aand solving gives S 2 = ( 5 V ∗ 3 A ) 2 = 225 ( V A ) 2 {\displaystyle S^{2}=(5V*3A)^{2}=225(VA)^{2}}
Q = P 2 − Q 2 {\displaystyle Q={\sqrt {P^{2}-Q^{2}}}}
Z t h = N 1 N 2 e 2 N 2 N 1 i 2 {\displaystyle {Z_{th}}={\frac {{\frac {N_{1}}{N_{2}}}{e_{2}}}{{\frac {N_{2}}{N_{1}}}{i_{2}}}}}
