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MUTUAL INDUCTANCE AND TRANSFORMERS

[CHAP. 14

Supplementary Problems 14.22

Two coupled coils, L1 ¼ 0:8 H and L2 ¼ 0:2 H, have a coeﬃcient of coupling k ¼ 0:90. inductance M and the turns ratio N1 =N2 . Ans: 0:36 H, 2

14.23

Two coupled coils, N1 ¼ 100 and N2 ¼ 800, have a coupling coeﬃcient k ¼ 0:85. current of 5.0 A in coil 2, the ﬂux is 2 ¼ 0:35 mWb. Find L1 , L2 , and M. Ans: 0:875 mH, 56 mH, 5.95 mH

14.24

Two identical coupled coils have an equivalent inductance of 80 mH when connected series aiding, and 35 mH in series opposing. Find L1 , L2 , M, and k. Ans: 28:8 mH, 28.8 mH, 11.25 mH, 0.392

14.25

Two coupled coils, with L1 ¼ 20 mH, L2 ¼ 10 mH, and k ¼ 0:50, are connected four diﬀerent ways: series aiding, series opposing, and parallel with both arrangements of winding sense. Obtain the equivalent inductances of the four connections. Ans: 44:1 mH, 15.9 mH, 9.47 mH, 3.39 mH

14.26

Write the mesh current equations for the coupled circuit shown in Fig. 14-37. circuit and write the same equations. Ans:

di1 þ R 3 i2 þ M dt di ðR2 þ R3 Þi2 þ L2 2 þ R3 i1 þ M dt

ðR1 þ R3 Þi1 þ L1

Find the mutual

With coil 1 open and a

Obtain the dotted equivalent

di2 ¼v dt di1 ¼v dt

Fig. 14-37 14.27

Write the phasor equation for the single-loop, coupled circuit shown in Fig. 14-38. Ans: ð j5 þ j3  j5:03  j8 þ 10ÞI ¼ 50 08

14.28

Obtain the dotted equivalent circuit for the coupled circuit of Fig. 14-38.

14.29

The three coupled coils shown in Fig. 14-40 have coupling coeﬃcients of 0.50. inductance between the terminals AB. Ans: 239 mH

14.30

Obtain two forms of the dotted equivalent circuit for the coupled coils shown in Fig. 14-40. Ans: See Fig. 14-41.

14.31

(a) Obtain the equivalent impedance at terminals AB of the coupled circuit shown in Fig. 14-42. Reverse the winding sense of one coil and repeat. Ans: ðaÞ 3:40 41:668 ; ðbÞ 2:54 5:378 

Ans:

See Fig. 14-39. Obtain the equivalent

(b)

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An