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CHAP. 14]

MUTUAL INDUCTANCE AND TRANSFORMERS

351

Fig. 14-28 The voltage across the j5 is partly conductive, from the currents I1 and I2 , and partly mutual, from current I1 in the 4  reactance. V ¼ ðI1 þ I2 Þð j5Þ þ I1 ð j3Þ ¼ 29:27 49:728 V Of course, the same voltage must exist across the capacitor: V ¼ I2 ðj8Þ ¼ 29:27 49:728 V

14.13 Obtain The´venin and Norton equivalent circuits at terminals ab for the coupled circuit shown in Fig. 14-29. In open circuit, a single clockwise loop current I is driven by the voltage source. I¼

10 08 ¼ 1:17 20:568 A 8 þ j3

Fig. 14-29 Then V 0 ¼ Ið j5 þ 4Þ  Ið j6Þ ¼ 4:82 34:608 V. To find the short-circuit current I 0 , two clockwise mesh currents are assumed, with I2 ¼ I 0 .    8 þ j3 10     4 þ j1 0  ¼ 0:559 83:398 A I0 ¼   8 þ j3 4 þ j1     4 þ j1 7 þ j5 

and

Z0 ¼

V0 4:82 34:608 ¼ 8:62 48:798  ¼ I0 0:559 83:398

The equivalent circuits are pictured in Fig. 14-30.

14.14 Obtain a conductively coupled equivalent circuit for the magnetically coupled circuit shown in Fig. 14-31. Select mesh currents I1 and I2 as shown on the diagram and write the KVL equations in matrix form.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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