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14.22 Two coupled coils, L1 0:8 H and L2 0:2 H, have a coe cient of coupling k 0:90. inductance M and the turns ratio N1 =N2 . Ans: 0:36 H, 2 Two coupled coils, N1 100 and N2 800, have a coupling coe cient k 0:85. current of 5.0 A in coil 2, the ux is 2 0:35 mWb. Find L1 , L2 , and M. Ans: 0:875 mH, 56 mH, 5.95 mH Find the mutual
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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 Two coupled coils, with L1 20 mH, L2 10 mH, and k 0:50, are connected four di erent 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 Write the mesh current equations for the coupled circuit shown in Fig. 14-37. circuit and write the same equations. Ans: R1 R3 i1 L1 di1 R 3 i2 M dt di R2 R3 i2 L2 2 R3 i1 M dt di2 v dt di1 v dt Obtain the dotted equivalent
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Fig. 14-37 14.27 Write the phasor equation for the single-loop, coupled circuit shown in Fig. 14-38. Ans: j5 j3 j5:03 j8 10 I 50 08 Obtain the dotted equivalent circuit for the coupled circuit of Fig. 14-38. Ans: See Fig. 14-39. Obtain the equivalent
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The three coupled coils shown in Fig. 14-40 have coupling coe cients of 0.50. inductance between the terminals AB. Ans: 239 mH
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Obtain two forms of the dotted equivalent circuit for the coupled coils shown in Fig. 14-40. Ans: See Fig. 14-41. (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: a 3:40 41:668 ; b 2:54 5:378  (b)
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CHAP. 14]
MUTUAL INDUCTANCE AND TRANSFORMERS
Fig. 14-38
Fig. 14-39
Fig. 14-40
Fig. 14-41 14.32 In the coupled circuit shown in Fig. 14-43, nd V2 for which I1 0. What voltage appears at the 8  inductive reactance under this condition Ans: 141:4 458 V; 100 08 V (+ at dot)
Find the mutual reactance XM for the coupled circuit of Fig. 14-44, if the average power in the 5- resistor is 45.24 W. Ans: 4 
MUTUAL INDUCTANCE AND TRANSFORMERS
[CHAP. 14
Fig. 14-42
Fig. 14-43
Fig. 14-44 14.34 For the coupled circuit shown in Fig. 14-45, nd the components of the current I2 resulting from each source V1 and V2 . Ans: 0:77 112:68 A; 1:72 86:058 A
Fig. 14-45 14.35 Determine the coupling coe cient k in the circuit shown in Fig. 14-46, if the power in the 10- resistor is 32 W. Ans: 0:791 In (14a), replace a, X11 , X22 , and XM by their expressions in terms of X1 , X2 , and k, thereby obtaining (14b).
CHAP. 14]
MUTUAL INDUCTANCE AND TRANSFORMERS
Fig. 14-46 14.37 For the coupled circuit shown in Fig. 14-47, nd the input impedance at terminals ab. Ans: 3 j36:3 
Fig. 14-47 14.38 Find the input impedance at terminals ab of the coupled circuit shown in Fig. 14-48. Ans: 1 j1:5 
Fig. 14-48 14.39 Find the input impedance at terminals ab of the coupled circuit shown in Fig. 14-49. Ans: 6:22 j4:65 
Fig. 14-49
MUTUAL INDUCTANCE AND TRANSFORMERS
[CHAP. 14
Obtain Thevenin and Norton equivalent circuits at terminals ab of the coupled circuit shown in Fig. 14-50. Ans: V 0 7:07 458 V; I 0 1:04 27:98 A; Z 0 6:80 72:98 
Fig. 14-50
For the ideal transformer shown in Fig. 14-51, nd I1 , given IL1 10:0 08 A Ans: 16:5 14:048 A IL2 10:0 36:878 A IL3 4:47 26:578 A
Fig. 14-51
When the secondary of the linear transformer shown in Fig. 14-52 is open-circulated, the primary current is I1 4:0 89:698 A. Find the coe cient of coupling k. Ans: 0:983
Fig. 14-52 14.43 For the ideal transformer shown in Fig. 14-53, nd I1 , given I2 50 36:878 A and I3 16 08 A. Ans: 26:6 34:298 A
Considering the autotransformer shown in Fig. 14-54 ideal, obtain the currents I1 , Icb , and Idc . Ans: 3:70 22:58 A; 2:12 86:718 A; 10:34 11:838 A
CHAP. 14]
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