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CHAP. 12]

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

Fig. 12-45

303

Fig. 12-46

The semicircular admittance locus of branch 2 has the radius r ¼ 1=2R ¼ 0:125 S. The total admittance is the sum of the fixed admittance Y1 and the variable admittance Y2 . In Fig. 12-47, the semicircular locus is added to the fixed complex number Y1 . The circuit resonance occurs at points a and b, where YT is real. YT ¼ 0:417  j0:088 þ

1 4  jXC

Fig. 12-47 which is real if XC2  11:36XC þ 16 ¼ 0 or XC1 ¼ 9:71 , XC2 ¼ 1:65 .

With ! ¼ 5000 rad/s, C1 ¼ 20:6 mF

C2 ¼ 121 mF

12.21 Show by locus diagrams that the magnitude of the voltage between points A and B in Fig. 12-48 is always one-half the magnitude of the applied voltage V as L is varied.

Fig. 12-48

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An