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MUTUAL INDUCTANCE AND TRANSFORMERS

[CHAP. 14

Fig. 14-30

Fig. 14-31 

3 þ j1 3  j2 3  j2 8 þ j6



I1 I2



 ¼

50 08 0



The impedances in Fig. 14-32 are selected to give the identical Z-matrix. Thus, since I1 and I2 pass through the common impedance, Zb , in opposite directions, Z12 in the matrix is Zb . Then, Zb ¼ 3 þ j2 . Since Z11 is to include all impedances through which I1 passes, 3 þ j1 ¼ Za þ ð3 þ j2Þ from which Za ¼ j1 .

Similarly, Z22 ¼ 8 þ j6 ¼ Zb þ Zc

and Zc ¼ 5 þ j4

.

Fig. 14-32

14.15 For the transformer circuit of Fig. 14-11(b), k ¼ 0:96, R1 ¼ 1:2 , R2 ¼ 0:3 , X1 ¼ 20 , X2 ¼ 5 , ZL ¼ 5:0 36:878 , and V2 ¼ 100 08 V. Obtain the coil emfs E1 and E2 , and the magnetizing current I . X11 ¼ ð1  kÞX1 ¼ ð1  0:96Þð20Þ ¼ 0:8  X22 ¼ ð1  kÞX2 ¼ 0:2  sffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi X1 ¼2 XM ¼ k X1 X2 ¼ 9:6  a¼ X2

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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