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The semicircular admittance locus of branch 2 has the radius r 1=2R 0:125 S. The total admittance is the sum of the xed admittance Y1 and the variable admittance Y2 . In Fig. 12-47, the semicircular locus is added to the xed complex number Y1 . The circuit resonance occurs at points a and b, where YT is real. YT 0:417 j0:088 1 4 jXC

Now, with the Thevenin equivalent in place, voltage division leads to VL Zeq sCgd gm 1 V Vi Zeq ZTh Th 1 ZTh =Zeq sCgd 8:40

1. (a) 2. (a) 3. (a) 5. (a) ; (b) ; (b) ; (b) ; (b) ; (c) ; (c) ; (c) ; (c) ; (d) ; (d) ; (d) ; (d) ; (e) ; (f) ; (e) ; (f)

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.

4. (a) more; (b) less 6. (c), (d), and (e) 7. (a) 5 to 7; (b) 6 to 10; (c) 4 to 10; (d) 3 to 9; (e) 2 to 8; ( f ) 1 to 13 8. (a) jB, jA, jC; (b) DF, EF, DE; (c) j3, j2, j1 9. (a) mjBAC mjACD; (b) AB BC 10. (a) BC, AB, AC; (b) jBOC, jAOB, jAOC; (c) AD, AB > CD, BC; (d) OG, OH, OJ

(8.41)

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Fig. 12-48

14

Branch-1 current I1 passes through two equal resistors R. Thus A is the midpoint on the phasor V, as shown in Fig. 12-49.

Rearranging (8.40) and using (8.41), we get Av s sCgd gm VL Vi s Cds Cgd gds GD GL 8:42

1. (a) Ornament, jewelry, ring, wedding ring; (b) vehicle, automobile, commercial automobile, taxi; (c) polygon, quadrilateral, parallelogram, rhombus; (d) angle, obtuse angle, obtuse triangle, isosceles obtuse triangle 2. (a) A regular polygon is an equilateral and an equiangular polygon. (b) An isosceles triangle is a triangle having at least two congruent sides.

Fig. 12-49 Branch 2 has a semicircular Y-locus [see Fig. 12-28(c)]. Then the current locus is also semicircular, as shown in Fig. 12.50(a). The voltage phasor diagram, Fig. 12-50(b), consists of the voltage across the inductance, VBN , and the voltage across R1 , VMB . The two voltages add vectorially, V VMN VBN VMB

(b) From (8.42), the high-frequency cuto point is obviously !H gds GD GL Cds Cgd 8:43

(c) A pentagon is a polygon having five sides. (d) A rectangle is a parallelogram having one right angle. (e) An inscribed angle is an angle formed by two chords and having its vertex on the circumference of the circle. ( f ) A parallelogram is a quadrilateral whose opposite sides are parallel. (g) An obtuse angle is an angle larger than a right angle and less than a straight angle. 3. (a) x 2 4; (b) 3y 15; (c) she does not love you; (d) his mark was not more than 65; (e) Joe is not heavier than Dick; ( f ) a b c 4. (a) A nonsquare does not have congruent diagonals. False (for example, when applied to a rectangle or a regular pentagon). (b) A non-equiangular triangle is not equilateral. True. (c) A person who is not a bachelor is a married person. This inverse is false when applied to an unmarried female. (d) A number that is not zero is a positive number. This inverse is false when applied to negative numbers. 5. (a) (b) (c) (d) Converse true, inverse true, contrapositive true Converse false, inverse false, contrapositive true Converse true, inverse true, contrapositive true Converse false, inverse false, contrapositive true

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